SOLUTION: x squared-x-6=0

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Question 96893: x squared-x-6=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve x%5E2-x-6=0 ( notice a=1, b=-1, and c=-6)

x+=+%28--1+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A-6+%29%29%2F%282%2A1%29 Plug in a=1, b=-1, and c=-6



x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A-6+%29%29%2F%282%2A1%29 Negate -1 to get 1



x+=+%281+%2B-+sqrt%28+1-4%2A1%2A-6+%29%29%2F%282%2A1%29 Square -1 to get 1 (note: remember when you square -1, you must square the negative as well. This is because %28-1%29%5E2=-1%2A-1=1.)



x+=+%281+%2B-+sqrt%28+1%2B24+%29%29%2F%282%2A1%29 Multiply -4%2A-6%2A1 to get 24



x+=+%281+%2B-+sqrt%28+25+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%281+%2B-+5%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%281+%2B-+5%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%281+%2B+5%29%2F2 or x+=+%281+-+5%29%2F2

Lets look at the first part:

x=%281+%2B+5%29%2F2

x=6%2F2 Add the terms in the numerator
x=3 Divide

So one answer is
x=3



Now lets look at the second part:

x=%281+-+5%29%2F2

x=-4%2F2 Subtract the terms in the numerator
x=-2 Divide

So another answer is
x=-2

So our solutions are:
x=3 or x=-2

Notice when we graph x%5E2-x-6, we get:

+graph%28+500%2C+500%2C+-12%2C+13%2C+-12%2C+13%2C1%2Ax%5E2%2B-1%2Ax%2B-6%29+

and we can see that the roots are x=3 and x=-2. This verifies our answer