SOLUTION: x<sup>2</sup> = x + 110

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: x<sup>2</sup> = x + 110      Log On


   

Question 36778: x2 = x + 110
Answer by vidhyak(98) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 = x + 110
x^2 - x - 110 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B-110+=+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=%28-1%29%5E2-4%2A1%2A-110=441.

Discriminant d=441 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+441+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+441+%29%29%2F2%5C1+=+11
x%5B2%5D+=+%28-%28-1%29-sqrt%28+441+%29%29%2F2%5C1+=+-10

Quadratic expression 1x%5E2%2B-1x%2B-110 can be factored:
1x%5E2%2B-1x%2B-110+=+1%28x-11%29%2A%28x--10%29
Again, the answer is: 11, -10. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-110+%29