SOLUTION: Use the quadratic formula to solve the equation x^2-4x-9=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Use the quadratic formula to solve the equation x^2-4x-9=0      Log On


   

Question 344602: Use the quadratic formula to solve the equation x^2-4x-9=0
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-4x-9=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-9+=+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=%28-4%29%5E2-4%2A1%2A-9=52.

Discriminant d=52 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+52+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+52+%29%29%2F2%5C1+=+5.60555127546399
x%5B2%5D+=+%28-%28-4%29-sqrt%28+52+%29%29%2F2%5C1+=+-1.60555127546399

Quadratic expression 1x%5E2%2B-4x%2B-9 can be factored:
1x%5E2%2B-4x%2B-9+=+1%28x-5.60555127546399%29%2A%28x--1.60555127546399%29
Again, the answer is: 5.60555127546399, -1.60555127546399. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-9+%29