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

$x=-1$ or 10

Algebra

Chapter 1

THE INTEGERS

Section 7

Quadratic Equations with Integral Roots

The Integers

Equations and Inequalities

Polynomials

Campbell University

Baylor University

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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'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't forget to keep the signs. We also need them to add to the negative not so list of factors a tent when it'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's not, it's negative. We just need to test some of the combinations. So let's say the one is negative. That would give us positive nines and I can't work. Let's say this tale is negative. That would give most negative nine. So we know this is our combination. We'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'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'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'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'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's gonna be negative one or 10.

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