SOLUTION: log5(x^2+x+4)=2

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Question 166806: log5(x^2+x+4)=2
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
log5(x^2+x+4)=2
x^2+x+4 = 5^2
x^2+x+4 = 25
x^2+x-21 = 0
Since we can't factor, we must use the quadratic equation.
Doing so will yield:
x = {4.110, -5.110}
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-21+=+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=%281%29%5E2-4%2A1%2A-21=85.

Discriminant d=85 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+85+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+85+%29%29%2F2%5C1+=+4.10977222864644
x%5B2%5D+=+%28-%281%29-sqrt%28+85+%29%29%2F2%5C1+=+-5.10977222864644

Quadratic expression 1x%5E2%2B1x%2B-21 can be factored:
1x%5E2%2B1x%2B-21+=+1%28x-4.10977222864644%29%2A%28x--5.10977222864644%29
Again, the answer is: 4.10977222864644, -5.10977222864644. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-21+%29