SOLUTION: Hi I would like to know the formula for working out x squared = x + 6. If you can answer my question, I am very thankful.

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Question 23507: Hi I would like to know the formula for working out x squared = x + 6. If you can answer my question, I am very thankful.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
This is a quadratic equation x%5E2+=+x%2B6 so you might be thinking of the quadratic formula that looks like this:x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ . However, this problem just might factor, and this is MUCH easier than the quadratic formula when the problem factors!

x%5E2+=+x%2B6

The first step is to set the equation equal to zero. You can either take everything to the right side or the left side, but I recommend that you arrange the terms so the x%5E2 term is positive. In this case, it means to take everything to the left side. Subtract x and 6 from both sides:
x%5E2+=+x%2B6
x%5E2-x+-6+=+x%2B6-x+-6
x%5E2+-+x+-6=0

This just happens to factor!
%28x-3%29%28x%2B2%29+=0

There are TWO solutions:
x-3 = 0, so x= 3
x+2 = 0, so x=-2

Final answer: x= 3 or x= -2

R^2 at SCC