in-9-26-solve-each-quadratic-equation-by-completing-the-square-express-the-answer-in-simplest-radi-2

Question

In $9-26,$ solve each quadratic equation by completing the square. Express the answer in simplest radical form.
$$
x^{2}+6 x+4=0
$$

Aditya Balasubramanian · Accepted Answer

So we have the function X squared plus six X plus four equals zero expression, that is. And we want to be able to solve the equation. Right? And you want to completion scripts. So what we would do is we would find a square or root, that adds to success. And I&#x27;ll be three X. Right? So you, that&#x27;s 1,000,000. That red pen makes a little more clear. We would get X Plus three squared, right? Did you get X squared? Plus three X plus three X, that B plus effects and then plus nine. Right. So right here we have a four, not a nine. So in order to account for that, you&#x27;II write this as X squared plus six X, we want a nine on this left side so we can isolate the experts to be squared so we&#x27;d be X squared plus x X plus nine. And since it&#x27;s four in total, you would want to put a negative. We&#x27;re sorry. You wanna put five over here. Since nine minus five could bring the final duel upside. This becomes floor. So what you would get is explosive. It&#x27;s weird. When you foil it, you&#x27;ll see that X squared plus six X plus nine is what you&#x27;ll get. So you use this X plus three Squared equals five was squared about size so that we can actually solve for X two. Solutions for five would be plus or minus Route five. Right, because we&#x27;re solving for a square root from the square and breeding three over the other side. That&#x27;s it, that is accident simplest form.

Foster Wisusik · Answer

Okay, This question wants us to solve the following quadratic. So we&#x27;re going to use the method of completing the square which turns X squared plus B x plus e into Vertex for a Times X plus d squared plus e. And we said D is defined to be be over to a and e is defined as C minus B squared over for a So let&#x27;s calculate these constants for our quadratic and Palladian. So we said that d is be over to a which in our example bees negative six days, one so d is negative three and then e is to minus B squared, which is 36 over for a So we get tu minus nine, which is negative seven. So are quadratic can now be it written in this reduced form as X minus three quantity squared minus seven is equal to zero, cause we just plugged into our complete the square form after we found D and E. So now we&#x27;re gonna add seven double sides to get X minus. Three squared is equal to seven or X minus three is equal to plus or minus the square root of seven. So now we&#x27;re gonna get to solutions we get one branch for X minus three equals positive Square seven and one branch for X minus three equals negative Route seven. So let&#x27;s just add three double sides to get our solutions of X equals three plus Route seven and X equals three minus Route seven and those air answers.

Foster Wisusik · Answer

Okay, This question would like us to solve the following quadratic. So to start, we&#x27;re gonna use to complete the square method which turns a general quadratic X squared plus B x plus e into a form that&#x27;s easier to solve. Equations with a times X plus d squared plus e for some constant. Do you? A. So we said that D is equal to be over to A and E is equal to C minus B squared over four a. So now let&#x27;s find these d any values for our quadratic. So for D, that&#x27;s just be over to a which is negative for over two or negative, too. And then for E. We have C minus B squared over for a and that&#x27;s one minus the square to 16 and four times eight&#x27;s for, so we get one minus for more negative three. So now are quadratic turns into X minus two. All squared minus three equals zero, and that&#x27;s a much easier equation to solve. So now we get X minus two. Quantity squared is equal to three. When we add three of all sides, and then if we take the square root, we get X minus two is equal to plus or minus the square root of three. So we know that we have two solutions. We have X minus three. Person X minus two equals the positive squared of three and X minus two equals the negative squared of three. So adding to teach equation gives us one solution of two plus squared of three and another solution of two minus squared of three. And these are our answers.

Aditya Balasubramanian · Answer

So I hear we have a function to X squared minus six X plus three this equal to zero in order to use completing the square. Let&#x27;s start off by factoring this out right, you can&#x27;t. It&#x27;s hard to do this if you have a, um, a co option of two in the X squared. So it&#x27;s factor this two out. And if you factored to Alec, you can also factor two out of the six negative six x so it will become two times X squared, minus three X. Keep the three out of it for now. Thank you, Thank you. Now, if you take a look at this native free X, this is technically the second term of and expressed form or expanded form of apologetic expression, and you could use the roots Negative three halves number three house times two people, native three. So let&#x27;s get this room handy. Red pen over here. Let&#x27;s pretend we use X minus three halves squared. So what would occur if we would get two times X squared? I&#x27;m gonna write this expense. We have squared and expanded form. Just concede a little more clearly. X squared minus three X and then three have some students. We need this final term that is equal to nine forts, correct. So it&#x27;s at night worths, all right, red pen. And we also have to subtract 9/4. But since we don&#x27;t want to interfere with this nice little expression, you got going on the parentheses because it&#x27;s it&#x27;ll be clean to just simplify like that. Well, multiply that negative nine forts by two. So will become negative nine haves and leave it out of there so you can actually simplify this X squared minus three hacks plus 9/4 R X squared minus three X plus nine for it&#x27;s a little Easier. So let&#x27;s do that. Let&#x27;s it&#x27;s untracked nine haves and keep it on the outside and then once again at that three from before and we would get that school gets two times X minus three halves squared not to add the equal zero. Originally, colleges that you get two times X minus three zero X rays. Three Scored the expense we have squared. That&#x27;s not very clear, but remember, that&#x27;s just a negative two halves right there. Tim&#x27;s excited. You have squared, um, native nine halves, plus the results of six hands so it would be minus three. Have negative naps plus six absence. Major three has men. That was a zero just lining up the science of clarity. And then what we would that have to do is solve for X right. You want to find X in its simplest form. So we would get two plums. X ministry have squared. Been that native three halves over. You have the right side. Then you have x three have squared. It was three halves divided by to correct. So three warrants then square both sides. You get X equals Dr Emmett experience. They have equals. We have not moved three halves already, and we have first you if you&#x27;d say X minus three has because plus or minus root of 3/4 and therefore X equals closer minus root 3/4 plus three hands and that is it. That is X we&#x27;re solving for X that is using competing square. And initially we had a lot of factoring you do, and this is a little trickier than if you had a coefficient of one, but that whenever you see a coefficient that it&#x27;s not one you&#x27;d have to know to back here. Now what&#x27;s it

Foster Wisusik · Answer

Okay, This question would like us to solve the following quadratic. So to do this, we&#x27;re going to use the method of completing the square which has seen here converts a general quadratic toe one in Vertex form. And to do this we need are constants DND, where d is be over to a and e is C minus B squared over four a. So now all we need to do is find these constants so d is be over to a which doing this It&#x27;s negative. 6/4 or negative three halves and then e is C minus. B squared over four a, which is three minus 36 over eight. And that could be simplified further, using a common denominator knowing that three is 24 8th to negative 12 8th which is again negative three has. So now we can just write this as are factored form, so we have two times X minus three halves squared minus three halves equals zero or now we can start solving. Add three habitable sides to get two times X minus three halves squared equals three halves, then divide by two to get X minus. Three halves squared is equal to 3/4 four x minus 3/4 is equal to Route three over to because the square root of forced to and then, of course, this is plus or minus squared of three. So now we have two branches. We have X minus three halves equals positive, 3/2, and then we have the negative. Branch X minus three halves equals negative Route 3/2. So if we do this, we get X is equal to three, plus Route 3/2 and X equals three minus root 3/2. And again, I&#x27;m just writing over our common denominator of to combining these fractions.

Aditya Balasubramanian · Answer

through here of s squared minus eight X plus four equals zero. And you&#x27;re that second term right there. When you do find a route that adds today, David X and that would be negative for X. A negative four inch times to you with your ex. When you Foyle, you&#x27;ll see what I mean. Let&#x27;s therefore use X minutes four squared so fearless you&#x27;d get X squared minus for X and a number minus What should be negative X But then also you get a plus 16 event. I do not see a plus 16 over here. All I see is a plus four. So you know what? Let&#x27;s rewrite this extraction so we can create AA plus 16 on the left side and therefore used in the square. But this you&#x27;re right. This is X squared minus eight banks plus 16. Let&#x27;s isolate that X minus four squared on one side and you notice how originally it was a four. If you put a 12 on this right side right here, you&#x27;ll see the 16 minus 12. If you bring that total over and you get that original expression when you isolate zero on the right side and simplify this. You&#x27;ll see he&#x27;ll become X minus four squared calls. 12th right square Both sides X minus four. You get two solutions you have plus or minus because you&#x27;re solving for and X from a square, you have to account for two solutions and become plus or minus two right squared of four grand. Four factors into 12 square to force to 23 so X therefore equals plus or minus +23 Bring the four over to the right side was for that is ext in its simplest form.

Problem

In $9-26,$ solve each quadratic equation by compl…

Problem 16 Medium Difficulty

In $9-26,$ solve each quadratic equation by completing the square. Express the answer in simplest radical form.
$$
x^{2}+6 x+4=0
$$

Answer

$-3+\sqrt{5}$ and $-3-\sqrt{5}$

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Absolute Value - Example 1

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$-3+\sqrt{5}$ and $-3-\sqrt{5}$

Algebra 2 and Trigonometry

Catherine R.

Anna Marie V.

Heather Z.

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Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Anna Marie V.

Heather Z.

Kristen K.

Ann Xavier Gantert

Algebra 2 and Trigonometry