SOLUTION: Can you please show me how to solve this equation using the quadratic formula (x-5)(x+1) = 4

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Can you please show me how to solve this equation using the quadratic formula (x-5)(x+1) = 4      Log On


   

Question 171582: Can you please show me how to solve this equation using the quadratic formula
(x-5)(x+1) = 4
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Can you please show me how to solve this equation using the quadratic formula
(x-5)(x+1) = 4
--------------
get it into quadratic form. Multiply the binomials.
x^2 - 4x - 5 = 4
x^2 - 4x - 9 = 0 (quadratic form)
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
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+=+%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


It's 2 + sqrt(13)
and 2 - sqrt(13)