Solve each equation in Exercises 1 - 14 by factoring. 7 - 7x =...

Question

Solve each equation in Exercises 1 - 14 by factoring. 7 - 7x = (3x + 2)(x - 1)

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we have the equation X squared minus six X plus eight is equal to two X plus 17. And we want to solve for X by factoring so in this case we're trying to get values of X. And we have X terms on both the left hand side and the right hand side. So in order to solve by factoring I'm going to get all of my terms on one side. So I can then factor that new equation Suffice, attract by two x - On both sides. My right hand side becomes zero and my left hand side is now X squared and I have negative six X minus two X. Which gives me negative eight X. And I have positive eight minus 17. So that gives me -9. So now you can see I have this new equation with all my terms on the left hand side and it's also a quadratic equation. So recall that when we're factoring a quadratic equation in this case I want the terms that show up in my factor terms to multiply to get negative nine And add to get -8. So if I use nine and negative one, Those multiply to get -9. And if I add nine and negative one I get positive eight. So I know I need to switch the sign on these. So now if I add negative nine and one I get negative eight. And if I multiply negative nine and positive one I get negative nine still. So now I know that I need to include negative nine and one in my factor terms. So my factor terms become x - times x plus one. Now you can see I have to factor terms that I can solve separately to get values for X. So first I have X -9 equal to zero. If I add nine I get X is equal to positive nine and then I have X plus one is equal to zero. If I subtract one I get X is equal to negative one. So here you can see I found two values for X. So X could either be negative one or 9. So this is my final answer for solving the equation by factoring and you can see that this alliance with answer choice B. So hopefully this video helped and see you next time.

Solve each equation in Exercises 1 - 14 by factoring. 7 - 7x = (3x + 2)(x - 1)

Key Concepts

Factoring Quadratic Equations

Setting Equations to Zero

Zero-Product Property

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