SOLUTION: Solve 14x=x^2+36 . Thanks!

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Question 709122: Solve 14x=x^2+36 . Thanks!
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Solve
14x=x^2+36
0=x^2-14x+36
since you can't factor, you can apply the quadratic formula to get:
x = {10.61, 3.39}
.
details of quadratic formula follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-14x%2B36+=+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=%28-14%29%5E2-4%2A1%2A36=52.

Discriminant d=52 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--14%2B-sqrt%28+52+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-14%29%2Bsqrt%28+52+%29%29%2F2%5C1+=+10.605551275464
x%5B2%5D+=+%28-%28-14%29-sqrt%28+52+%29%29%2F2%5C1+=+3.39444872453601

Quadratic expression 1x%5E2%2B-14x%2B36 can be factored:
1x%5E2%2B-14x%2B36+=+1%28x-10.605551275464%29%2A%28x-3.39444872453601%29
Again, the answer is: 10.605551275464, 3.39444872453601. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-14%2Ax%2B36+%29