SOLUTION: How do you solve x squared minus 6x minus 15 equals 0?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: How do you solve x squared minus 6x minus 15 equals 0?      Log On


   

Question 916871: How do you solve x squared minus 6x minus 15 equals 0?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+-+6x+-+15+=+0
---
You can complete the square, or use the quadratic equation.
Those 2 methods always work.
----
x%5E2+-+6x+-+15+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B-15+=+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=%28-6%29%5E2-4%2A1%2A-15=96.

Discriminant d=96 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+96+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+96+%29%29%2F2%5C1+=+7.89897948556636
x%5B2%5D+=+%28-%28-6%29-sqrt%28+96+%29%29%2F2%5C1+=+-1.89897948556636

Quadratic expression 1x%5E2%2B-6x%2B-15 can be factored:
1x%5E2%2B-6x%2B-15+=+%28x-7.89897948556636%29%2A%28x--1.89897948556636%29
Again, the answer is: 7.89897948556636, -1.89897948556636. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B-15+%29