SOLUTION: x^2 + 8x = 9.

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Question 223783: x^2 + 8x = 9.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2B+8x+=+9

Step 1. Subtract 9 from both sides of the equation to get a quadratic equation

x%5E2+%2B+8x-9+=9-9

x%5E2+%2B+8x-9+=0

Step 2. To solve, use the quadratic formula given as

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

where a=1, b=8, and c=-9

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8x%2B-9+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%288%29%5E2-4%2A1%2A-9=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+100+%29%29%2F2%5C1+=+1
x%5B2%5D+=+%28-%288%29-sqrt%28+100+%29%29%2F2%5C1+=+-9

Quadratic expression 1x%5E2%2B8x%2B-9 can be factored:
1x%5E2%2B8x%2B-9+=+1%28x-1%29%2A%28x--9%29
Again, the answer is: 1, -9. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B-9+%29



I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

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