solve-and-check-each-of-the-equations-3-x2-5-x36-2-x

Question

Solve and check each of the equations.
$3 x^{2}-5 x=36-2 x$

M S · Accepted Answer

So we want to stop and check this equation. So the first step is to get everything on one side, someone to subtract 36 from both sides. And I&#x27;m going to add two extra both sides. When did his only one step? So there are three X squared minus biotics. They would have plus two X and one is 36 uncle Zero and have a combined like terms. So three ex cleared minus three X minus 36. So we wants it back to this. But I don&#x27;t really like dealing with big numbers, so I&#x27;m gonna factor out this three. So that&#x27;s the greatest. Call me factor. Phony. Incirlik with X squared minus X minus 12. This is much easier to factor than those big numbers we would have dealt with. So the first step is to separate our middle term here. Our middle term in this case will be the minus X that we want to separate this. So we need the little park prohibition times our last term, and we get negative 12 there. We know we need to adds a negative one. So the factors of 12 or one in 12 to in six and three on board, and we know that we need It&#x27;s a multiply through a negative number. So one of the times have to be negative already knows not gonna be one and 12 because it has the ad said negative one and the other too far apart. These are also too far apart. So we know we&#x27;re dealing with three and four and only one of these numbers could be negative. So the three is negative for Money. Street is as positive one from you, too. Negative one. So we know that the four must be negative. History minus four gives us the negative voice. So we split apart in middle turn. You have X squared close three x minus for X and they bring down at minus school. You know, three And they were gonna group our first he turns a group or a second too. But I want it back throughout the greatest calming factor. So have X Times X plus three. But then here in factor out for someone sport we left with explosive three because we have the same term here in here. You know, there were on the right step, so I have three times X plus three times X minus four with the equal to zero. And we&#x27;ve factored this completely. So check this. We need Thio that each factor equal to zero distinctly. So we have exposed three equal zero. If X minus four equals zero, we get ignored a three because it doesn&#x27;t have any very well associated with it. So right here, gonna subtracted from both sides. They will have X equals negative three. And here we are at boarding boats. Thought it will have X equals positive for So the trick. We just put that back into our original equation here. So I&#x27;m gonna play in that unit three first. So we have three toes. Anything you squared minus father sounds negative. Three equals 36 months. Two times negative. Three. You have three times nine plus 15 people&#x27;s 36 plus six. That&#x27;s totally seven plus 15. And that 42. And this morning, too. And because I equal each other, you know that next minus three is the correct answer. We also need to check our board. So we have three times four. We&#x27;re minus five times for equals 36 months. Two times four, Mr. B. three terms, 16 minus 20 equals 36 1 is a This would be 48 minus 20 and this will be 28 minute 48. Minus 20 gives us 28 and she&#x27;s also correct, So know that X congee negative.

Eva R · Answer

So we&#x27;re going to set this up as a giant, rational equation that we&#x27;re gonna need to solve. And it would be a whole heck of a lot easier if I could just clear out that denominator. So what I&#x27;m gonna do is I&#x27;m gonna find the LCD or the least common denominator. Basically, I want to keep in mind that this is X times X minus one. So these are the same, but this has an ex, so I&#x27;m gonna go ahead and multiply every single thing by this entire denominator that will clear them out from each fraction. So this 1st 1 will get multiplied by X times X minus one. This one will get most plied by X times X minus one And so will this one. Okay, In doing that, I&#x27;m going to be able to ditch the ex Beatle stitch the excellence one. So this is all gone and I&#x27;m left with five. And this one that X men, it&#x27;s one and the x minus. One will cross off, so I&#x27;m left with three ex. And in this one, nothing crosses off. So I&#x27;m left with the whole thing. Six X Times X minus one next. All simplify. So I have five plus three X equals six X squared, minus six x. Let&#x27;s go ahead and move everything to the right. Since I&#x27;m dealing with a quadratic, I&#x27;m gonna wanna use this. You&#x27;re a product property. So zero equals six x square. When I move the three over, it&#x27;ll become a negative. So minus nine X minus five that I want to decide if this is fact herbal. If it is fact herbal, I would be looking for something that multiplies to be negative. 30 since I want to look at a NC and an ABS to be negative nine. So are there two values that multiply to be negative 30 and had to be negative? Nine. Hopefully you thought for a second and realized No, there isn&#x27;t. So we&#x27;re gonna have to use the quadratic formula. Let&#x27;s go ahead and do that. Good old X equals negative B plus or minus the square root of B squared minus for a C all over two A. All right, here we go. So X equals negative B. That&#x27;s a positive nine in this case, plus or minus the square root of B squared. So b squared is negative. Nine square 81 minus four times a which is six times C, which is negative. Five all over two A. So two times six X equals nine plus or minus the square root of 81 then we have a negative negative. So positive and we&#x27;re gonna D&#x27;oh! Four times six times five 1 20 all divided by 12. Now we&#x27;re looking at X equals nine plus or minus the square root of 201 over 12. And that&#x27;s pretty simple as far as it goes. So we&#x27;re gonna keep this answer. But we do want to check that those values will work with our original equation. So basically, we just need to make sure there are no domain restrictions and the domain restrictions from this part would have been zero, and this part would have been one. This is neither of those values. So we have the correct answer here as nine plus or minus the square root of 201 over 12th

K B · Answer

So this punching me of three over to axe minus five over three. X equals two. Listen to what we can do is we&#x27;re gonna multiply everything here all by six x because this is this will get rid of Lord A nominee. So here we end up with 18 hacks over to ex, which is just nine minus to them, they would have 30 actually. Were three x minus 10 equals 12 acts. From this, we can determine the X equals negative 1 12 Check our solution. We have three over three over negative to over 12 which is gonna be the same as negative. 36 over to our native 18. I mean minus five over. So I put this up five over. Negative three over 12. Which can be, which is the same. This will be negative. 18 lost for me, which is gonna be equal to two. And this does where our solution is. X equals negative one

Eric Solomon · Answer

Let&#x27;s solve the equation to divide up three Divided by two X minus two divided by three x equal spot. First thing we&#x27;re gonna do is I&#x27;m gonna multiply through by a common denominator. In this case, that common denominator is gonna be six to take care of that, you and the three. And then we&#x27;ll multiply by X to take care of these accents. So most by both sides by six acts that&#x27;s going to give us while six X divided by two ex will make a three. So we&#x27;re gonna have three times three, which is nine. Six x divided by three X is going to give us too. So we&#x27;re gonna have nine minus for equals, five times x X is 30 x simple. Find the left side we get five equals 30 x And if we divide both sides by 30 that gives us X equals five divided by 30 which can be seen. Britain has one divided by six. So let&#x27;s check our work If we plug one divided by six and two Original equation. We get three divided by two times one. Divide about six minus two divided by three times one divided by six, which is equal to five. This two times one about a best six we can write is 1/3. So we get three divided by 1/3 minus 23 times 16 we can rewrite as 1/2. So two divided by 1/2 equals five. Dividing by a fraction is the same is multiplying by the inverse of that fraction. So we can write this as three times three when we can write, this has two times two equals five. This gives us nine minus four equals five, which gives us five equals five, and so one sex is our answer.

Heather Zimmers · Answer

to solve this equation, we can rewrite the equation so that each side is the power of six. So we have six to the X power equals six squared since 36 is six squared. Now we set the exponents equal to each other, and we have x equal to

Grace Muhihu · Answer

Okay, So to solve the following equation, I&#x27;m gonna multiply both sides by five. So with that, I&#x27;m going to get three X minus 30 is equal to five packs. So when I&#x27;m gonna bring the three x to the right hand side, still have negative 30 is equal to two x Saman. If I divide both sides by two, I get that too is equal to or excusing. The X is equal to negative 15. So now I&#x27;m gonna check and see if that is correct. So we have three times negative. 15 over five minus six is equal to negative 15. So with us, we have negative 15/5, which is negative. Three times three is negative. Nine and then minus six. We know is negative. 15. So this is correct. So x is negative 15

Problem

Solve and check each of the equations. $7=x(8-x)$

Problem 12 Medium Difficulty

Solve and check each of the equations.
$3 x^{2}-5 x=36-2 x$

Answer

$x=-3$ or 4

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Catherine R.

Kayleah T.

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Absolute Value - Example 1

Absolute Value - Example 2

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$x=-3$ or 4

Algebra 2 and Trigonometry

Catherine R.

Kayleah T.

Maria G.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Catherine R.

Kayleah T.

Maria G.

Michael J.

Ann Xavier Gantert

Algebra 2 and Trigonometry