SOLUTION: don't know how to solve this!!! x squared- 5x-6

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Question 88859: don't know how to solve this!!!
x squared- 5x-6
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%5E2-5%2Ax-6=0 ( notice a=1, b=-5, and c=-6)

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



x+=+%285+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A-6+%29%29%2F%282%2A1%29 Negate -5 to get 5



x+=+%285+%2B-+sqrt%28+25-4%2A1%2A-6+%29%29%2F%282%2A1%29 Square -5 to get 25



x+=+%285+%2B-+sqrt%28+25%2B24+%29%29%2F%282%2A1%29 Multiply -4%2A-6%2A1 to get 24



x+=+%285+%2B-+sqrt%28+49+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%285+%2B-+7%29%2F%282%2A1%29 Simplify the square root



x+=+%285+%2B-+7%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%285+%2B+7%29%2F2 or x+=+%285+-+7%29%2F2

Lets look at the first part:

x=%285+%2B+7%29%2F2

x=12%2F2 Add the terms in the numerator
x=6 Divide

So one answer is
x=6



Now lets look at the second part:

x=%285+-+7%29%2F2

x=-2%2F2 Subtract the terms in the numerator
x=-1 Divide

So another answer is
x=-1

So our solutions are:
x=6 or x=-1

Notice when we graph x%5E2-5%2Ax-6, we get:

+graph%28+500%2C+500%2C+-11%2C+16%2C+-11%2C+16%2C1%2Ax%5E2%2B-5%2Ax%2B-6%29+

and we can see that the roots are x=6 and x=-1. This verifies our answer