Solve each equation using the zero-factor property. See Example 1...

Question

Solve each equation using the zero-factor property. See Example 1. -6x^2 + 7x = -10

Accepted Answer

Hello, everyone. We're going to use the zero factor rule to solve the quadratic equation. Negative eight X squared plus 17 X equals negative 21. So the first thing I recall about the zero factor rule is that I want my equation to equal zero. Currently, it does not. So I'm gonna make it equal zero by adding 21 to both sides. So now I have negative eight X squared plus 17 X plus 21 equals zero. The next part of the zero factor role is to factor. So factoring the left hand side, I'm going to factor out a negative one first. This way I don't have a negative leading coefficient to deal with and it'll make factoring it into Bino meals a little easier. So I factored out negative one. So I have negative one times eight X squared minus 17 X minus 21. Keeping that negative one on the outside. I'm gonna break my try no meal into by no meals. And if this takes you a couple tries to find the right combination, that is absolutely fine. Sometimes it just takes practice to find the combinations that work quickest. So this is going to be eight X plus seven and X minus three. So right now in factored form, I have it as negative one times eight X plus seven times X minus three equals zero. So now I'm going to set each set of parentheses equal to zero to find out what my X values are negative. One does not need to be equal to zero because there is no X value there. If we had factored out an X, I would have set it equal to zero. No, X no need to set it equal to zero. So eight x plus seven equals 0 and then X minus three equals zero, solving them each independently, eight X plus seven equals zero. I'm gonna subtract seven from both sides. eight x equals negative seven, divide both sides by eight. So one of our solutions is that x equals negative 7/8. There's one of them And then X - equals zero. I'm going to solve that by adding three to both sides And I get that x equals three. That should be the other part of our solution. Now that we have both values, we can look at our answer choices and this is answer choice. C have a nice day.

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Solve each equation using the zero-factor property. See Example 1. -6x^2 + 7x = -10