SOLUTION: I am trying to solve by using quadratic formula x^2-9x-4=6 I am confused on what to do with =6, do I rule it out when I begin simplifying? Please help

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Question 88233This question is from textbook algebra
: I am trying to solve by using quadratic formula
x^2-9x-4=6
I am confused on what to do with =6, do I rule it out when I begin simplifying?
Please help This question is from textbook algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-9x-4=6

x%5E2-9x-10=0 Subtract 6 from both sides

Now let's use the quadratic formula to solve for x:


Starting with the general quadratic

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

the general form of 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%5E2-9%2Ax-10=0 (notice a=1, b=-9, and c=-10)

x+=+%28--9+%2B-+sqrt%28+%28-9%29%5E2-4%2A1%2A-10+%29%29%2F%282%2A1%29 Plug in a=1, b=-9, and c=-10



x+=+%289+%2B-+sqrt%28+%28-9%29%5E2-4%2A1%2A-10+%29%29%2F%282%2A1%29 Negate -9 to get 9



x+=+%289+%2B-+sqrt%28+81-4%2A1%2A-10+%29%29%2F%282%2A1%29 Square -9 to get 81



x+=+%289+%2B-+sqrt%28+81%2B40+%29%29%2F%282%2A1%29 Multiply -4%2A-10%2A1 to get 40



x+=+%289+%2B-+sqrt%28+121+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)



x+=+%289+%2B-+11%29%2F%282%2A1%29 Simplify the square root



x+=+%289+%2B-+11%29%2F2 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

x+=+%289+%2B+11%29%2F2 or x+=+%289+-+11%29%2F2

Lets look at the first part:

x=20%2F2 Add the terms in the numerator
x=10 Divide

So one answer is
x=10
Now lets look at the second part:

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

So another answer is
x=-1

So our solutions are:
x=10 or x=-1

Notice when we graph x%5E2-9%2Ax-10 we get:

+graph%28+500%2C+500%2C+-11%2C+20%2C+-11%2C+20%2C1%2Ax%5E2%2B-9%2Ax%2B-10%29+

and we can see that the roots are x=10 and x=-1. This verifies our answer