SOLUTION: Solve the equation 5(x2−20) = 2x(3+x)−40, giving your answers to 5 decimal places

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Question 1005954: Solve the equation 5(x2−20) = 2x(3+x)−40,
giving your answers to 5 decimal places
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Use ^ (Shift 6) for exponents.
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Solve the equation 5(x^2 - 20) = 2x(3+x) - 40
5x^2 - 100 = 6x + 2x^2 - 40
3x^2 = 6x + 60
x^2 - 2x - 20 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-20+=+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=%28-2%29%5E2-4%2A1%2A-20=84.

Discriminant d=84 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+84+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+84+%29%29%2F2%5C1+=+5.58257569495584
x%5B2%5D+=+%28-%28-2%29-sqrt%28+84+%29%29%2F2%5C1+=+-3.58257569495584

Quadratic expression 1x%5E2%2B-2x%2B-20 can be factored:
1x%5E2%2B-2x%2B-20+=+%28x-5.58257569495584%29%2A%28x--3.58257569495584%29
Again, the answer is: 5.58257569495584, -3.58257569495584. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-20+%29