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 -> 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 449460: 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.)
2x^2=-2x+7
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!
2x2=-2x+7
2x2+2x-7=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B2x%2B-7+=+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=%282%29%5E2-4%2A2%2A-7=60.

Discriminant d=60 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+60+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+60+%29%29%2F2%5C2+=+1.43649167310371
x%5B2%5D+=+%28-%282%29-sqrt%28+60+%29%29%2F2%5C2+=+-2.43649167310371

Quadratic expression 2x%5E2%2B2x%2B-7 can be factored:
2x%5E2%2B2x%2B-7+=+2%28x-1.43649167310371%29%2A%28x--2.43649167310371%29
Again, the answer is: 1.43649167310371, -2.43649167310371. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B2%2Ax%2B-7+%29