SOLUTION: How do you change a problem such as, x^2-51=-2x, into a quadratic equation using the quadratic formula?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: How do you change a problem such as, x^2-51=-2x, into a quadratic equation using the quadratic formula?      Log On


   

Question 457233: How do you change a problem such as, x^2-51=-2x, into a quadratic equation using the quadratic formula?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
It is a quadratic equation now.
Do you want to solve it using the quadratic formula?
x^2+2x-51
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-51+=+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%2A1%2A-51=208.

Discriminant d=208 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+208+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+208+%29%29%2F2%5C1+=+6.21110255092798
x%5B2%5D+=+%28-%282%29-sqrt%28+208+%29%29%2F2%5C1+=+-8.21110255092798

Quadratic expression 1x%5E2%2B2x%2B-51 can be factored:
1x%5E2%2B2x%2B-51+=+1%28x-6.21110255092798%29%2A%28x--8.21110255092798%29
Again, the answer is: 6.21110255092798, -8.21110255092798. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-51+%29