solve-and-check-each-of-the-equations-x2-9-x10

Question

Solve and check each of the equations.
$x^{2}-9 x=10$

M S · Accepted Answer

so you wanna solve it? Took this equation so the first step will be to get this tin to the other side. Someone is attracting from both sides well, a big square minus my next monitor and equal zero. The only way we can saw is when the equal zero That&#x27;s bar. The first step was moved that tin. So now when he took back to our lives inside. So we need to split apart this middle term. And to do so, we need to multiply our coefficient times. Our last turn. Someone times negative 10 gives us negative. Don&#x27;t forget to keep the signs. We also need them to add to the negative not so list of factors a tent when it&#x27;s in in two and five. And because multiplication rules for negative we have a negative 10. That means only wanted to turn has to be negative. So it either has to be negative one or negative 10 with my boat, and because it&#x27;s not, it&#x27;s negative. We just need to test some of the combinations. So let&#x27;s say the one is negative. That would give us positive nines and I can&#x27;t work. Let&#x27;s say this tale is negative. That would give most negative nine. So we know this is our combination. We&#x27;re gonna split apart that middle term here. So x squared, minus X minus, No plus X place. One X is the one was positive minus 10 X and then bring down that minus 10 and said equal to zero. Now I factored advice to in factory Second, to hear from diverse with important except religion, politics plus one. They&#x27;re from the second to the greatest Tommy back. There would be negative 10. So we pull out and I get Stan and Willy for Dex plus one. And because this term here is the same as this term here, we know that we have explosive Lynn and then we bring down explain his tunes and equal to zero. So now we&#x27;re gonna set both of these factors equals zero distinctly So have express one equals zero an X minus Tanny zero. So piece of track limp about side to get X equals negative one. And if you had sent to both sides, we get X people&#x27;s positive. 10. What would you need to check to make sure that both of these solutions work? Someone a plug it into the original equation. So we are negative. One squared minus nine times negative one. And we wanted people. 10. The negative one square gives us positive one in negative buying times. Negative one gives us positive. Nine in one place. Nine. Does people tune? So this works out. We also need to play in our tune. So tense, weird minus not in terms. 10. Everyone&#x27;s equal saying, since word is 100 and they give nine times 10 gives us negative mind and 100 minus 90 was 10 and that does simpleton, so it&#x27;s gonna be negative one or 10.

Ankit Gupta · Answer

here we are given with the question act scared. Plus, then is a gold mine. Last night we can rewrite the questioners. Ex scared less dnx plus nine is equal to zero, which is in the forming. XK plus BX plus C is equal to zero now, using the quadratic form Love It&#x27;s which is minus B plus minus, for the values affects minus B plus minus under route. The scare minus four a. C but born no a. So substituting all the values from the equation by comparing it to XK plus BX plus e. We have very these effects as minus B means minus 10 plus minus bays. Then so be scared will be 100 minus four into one into the value sees. Night and fourth line into war is equal to 36 for that too, which is equal to minus 10 plus minus. Undercoat. I had minor 36 will be 64 over to X is equal to minus 10 plus minus it over to, or I understand minus eight over toe and my understand less it over to. So the values off X will be when a 16 byte over which will be minus eight. I don&#x27;t Sorry. Minus 18 by two, which will be equal to minus nine. And I understand place it will be equal to minus two overdue, which will be equal to minus one. So the solution off the question is given us minus one and my next night, that&#x27;s it.

Amanda Stone · Answer

in this problem were given the equation. 10 equals negative nine minus X and were asked to stall for acts and check her answer. It&#x27;s the first thing I want to do is get all of my numbers toe one side of the equation and all of my variables to the other. So to do that, I&#x27;m going to add nine to both sides of my equation so that on my right side I only have exes. So if we do that thes nines will cancel out and we&#x27;re left with 10 plus nine on the left with it, which is 19 equals negative X. And the last thing I want to do here is get rid of that negative next to the axe. So I&#x27;m going to multiply both sides by negative ones that thes negatives will cancel out, and that will leave me with negative 19 equals acts or X equals negative 19. To check our answer, we just have to plug this back into our original equation. So 10 equals negative nine minus negative. 19 or 10 equals negative nine plus 19 which will give us 10 on both sides

Charles Carter · Answer

Okay, so this problem, except ask us to solve an equation X to the four minus 10 X Square plus nine equals zero. Okay. So we can factor this because it follows a quadratic pattern. So two numbers that multiply to give nine that add to give negative 10 would be negative night and negative. Lauren, it&#x27;s like I can rewrite this equation is X squared minus nine and X squared minus one, equaling zero. He&#x27;s both follow the difference of squares pattern, so we can rewrite this as X plus three times X minus three times x plus one times X minus one equaling zero. So each one of these factors works out pretty nicely, so that we can say that the four solutions are gonna be X equals plus and minus three and X equals cosine minus one. Okay, thank you very much.

Shaza Hammoud · Answer

and the questions required to solve the forming equation. So we have expert for my stand exported my last night. We don&#x27;t know how to solve directly the export for but since the leading term is export for is D is tthe e the power off the square power off export of two which is the middle term. So in other words, it&#x27;s export for the relation between the kneading ter and the middle term that export four is did middle term to the power off too. So now we will substitute why right wife or ex 12 to then instant off writing extraordinary. All substituted by with y and ex instead off export for a saluted with Why support off too. So the equation becomes quadratic as a result. So it&#x27;s wide apart off too minus then entered off export of toe All right, why and then plus nine peak was zero. So this is equality equation Now we want to solve it. You can use either the the quadratic formula or to complete the square for this occasion. In this case, I used the as you can see here I&#x27;ll use the quadratic formula, which is a dark substitution off the values off a BNC that can be obtained directly from this ah quality equation. So a is the is one, which is the confident off y squared B Is deacon efficient off? Why and see is the constant number. So now, So the value is depressed very off. Why will be minus B, which is minus 10? Let&#x27;s take first D plus sign square root, be it support off. To which here is the discriminative B squared minus for a C. The bee is minus Stan, so it&#x27;s minus. Then the board off too minus four a is one c is nine, and then it&#x27;s over. Two multiplied by a, which is one. So it&#x27;s computed minus with minus would be positive. So, Stan, plus what&#x27;s inside this great route as Manus Stan two Pork two is 100 minus. Former blood by nine is 36 so it&#x27;s 100 minus 36 this is 64 over too. So here is 10 or it&#x27;s a Tempus squared off 64 squared off 64 is eight, so eight plus 10 is 18 and 18. Over too is nine. So one of distributions off. That&#x27;s why I want equals tonight. The other solution is why too is just by changing design off. What Thea other sign the other side which is in the negative sign instead of the positive sign. So it would be 10 minus eight over too. In minus eight is two and two over too. But be one. So this is the first value of why and this is the can vary off. Why however we want the values off x So the first why is nine and the second way is one What we have to do is now to substitute export toe. Is it off? Why one at X 12 toe instead of white? Oh, how to do that? It&#x27;s simply why you want. You want that why one is not And we know that why is actually export of two so entered off What I write Export of two equals 29 and then I&#x27;ll take the square root off both sides to get rid of the power off to then X will be plus minus three. So the two solutions are one is most of three and other one is my surgery. So he is the 1st 2 solutions now for why too equals one. I&#x27;ll take also the servitude back. Why? As ex wart off too equals to one. Then take the square root off both sides to get rid of the power of two. Then X will be equals two dust minus one. So the other two solutions the thread on the fourth solution as plus minus one. So we have four solutions since its export for the doctor is export for which means that we have forced loose and here, in this case, we have four different rational solutions.

Bahar Tehranipoor · Answer

in this exercise. We want to solve this equation and checker answers. So to use a procedure that we&#x27;ve learned we want to get the base is the same. So we can rewrite this night of X as something three to the power of something so that we can solve for exponents. So we&#x27;ll keep the three to the X Plus to hear the same. And we know that nine itself is just free squared so we can rewrite the nine as three scramble of three squared to the X and we have a number to a power. And then that all of it it&#x27;s another power. We could just multiply those powers together so we can rewrite this as three to the explosives to equals free to the two times X, which is just two X here. So we&#x27;re solving for this equation. So all we did was rewrite nine to the ex with a base of three. Now we&#x27;re gonna solve for X Plus two equals two ex subtract extra bowl size. We get to equals X sore answer. As X equals two before we go and just circle it. Let&#x27;s just check in and see. That&#x27;s right butt plug in to hear we get three to the two plus two, which is 3 to 432 before is 81. Plug in to hear we get nine squared, which is 81 So ex Eagles to is, in fact, are correct Answer.

Problem

Solve and check each of the equations. $4-x(x-3)…

Problem 8 Medium Difficulty

Solve and check each of the equations.
$x^{2}-9 x=10$

Answer

$x=-1$ or 10

Related Courses

Algebra 2 and Trigonometry

Related Topics

Discussion

Top Algebra Educators

Grace H.

Anna Marie V.

Caleb E.

Maria G.

Algebra Courses

Absolute Value - Example 1

Absolute Value - Example 2

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

Ann Xavier Gantert

Algebra 2 and Trigonometry

Grace H.

Anna Marie V.

Caleb E.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$x=-1$ or 10

Algebra 2 and Trigonometry

Grace H.

Anna Marie V.

Caleb E.

Maria G.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Grace H.

Anna Marie V.

Caleb E.

Maria G.

Ann Xavier Gantert

Algebra 2 and Trigonometry