SOLUTION: x^2-x=6

Question 725237: x^2-x=6
Answer by erika514(39) (Show Source): You can put this solution on YOUR website!
Hi there....I love these problems. Here we go!
So first we are going to subtract 6 from both sides. We should have x^2-x-6 on one side and we are going to have zero on the other side of the equation because a quadratic equation is ALWAYS in the form ax^2+bx+c=0. Now we are going to factor this equation,and we should get (x-2)(x+3). We need to solve our two equations for x and set both equal to zero. Let's do x-2=0 first. In this equation we just add 2 to both sides to get x=2. Finally, we need to solve x+3=0 by subtracting 3 from both sides to get x= -3. BUT we need to check yet to make sure our solutions work. We'll start by plugging 2 in for x. We should have(2)^2-2-6=0, which simplifies to 4-2-6=0 which equals -2, and -2 does not equal zero! So this is not a solution. And...we have one more value to check. We will plug in -3 into the equation to get...(-3)^2-3-6=0, which simplifies to 9-3-6=0, which equals zero so this value works!! :) So our final solution for x is x= -3. Let me know if you have any questions.
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