SOLUTION: log base8 [(x+8)(x+9)]=2

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Question 527085: log base8 [(x+8)(x+9)]=2
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
log base8 [(x+8)(x+9)]=2
(x+8)(x+9) = 8^2
x^2+17x+72 = 64
x^2+17x+8 = 0
apply the "quadratic formula" to get:
x = {-0.484, -16.516}
we can throw out the -16.516 (extraneous) leaving:
x = -0.484
.
details of quadratic:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B17x%2B8+=+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=%2817%29%5E2-4%2A1%2A8=257.

Discriminant d=257 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-17%2B-sqrt%28+257+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2817%29%2Bsqrt%28+257+%29%29%2F2%5C1+=+-0.484390229059301
x%5B2%5D+=+%28-%2817%29-sqrt%28+257+%29%29%2F2%5C1+=+-16.5156097709407

Quadratic expression 1x%5E2%2B17x%2B8 can be factored:
1x%5E2%2B17x%2B8+=+1%28x--0.484390229059301%29%2A%28x--16.5156097709407%29
Again, the answer is: -0.484390229059301, -16.5156097709407. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B17%2Ax%2B8+%29