SOLUTION: Solve the following equation by using the quadratic formula. (Enter solutions from smallest to largest. If there is one solution with a multiplicity of two, enter it in both answer

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve the following equation by using the quadratic formula. (Enter solutions from smallest to largest. If there is one solution with a multiplicity of two, enter it in both answer      Log On


   

Question 449454: Solve the following equation by using the quadratic formula. (Enter solutions from smallest to largest. If there is one solution with a multiplicity of two, enter it in both answer boxes.)
(x-2)(x+1)=8
x = ?
x = ?
Please show me the steps to get the steps.
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
(x-2)(x+1)=8
x2-x-2=8
x2-x-10=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-10+=+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=%281%29%5E2-4%2A1%2A-10=41.

Discriminant d=41 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+41+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+41+%29%29%2F2%5C1+=+2.70156211871642
x%5B2%5D+=+%28-%281%29-sqrt%28+41+%29%29%2F2%5C1+=+-3.70156211871642

Quadratic expression 1x%5E2%2B1x%2B-10 can be factored:
1x%5E2%2B1x%2B-10+=+1%28x-2.70156211871642%29%2A%28x--3.70156211871642%29
Again, the answer is: 2.70156211871642, -3.70156211871642. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-10+%29