SOLUTION: what are the solutions of 4x^2-16x=16x-39

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Question 437282: what are the solutions of
4x^2-16x=16x-39
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
4x^2-16x=16x-39
4x^2-32x=-39
4x^2-32x+39 = 0
solve using the quadratic formula to get:
x = {6.5, 1.5}
.
Details of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-32x%2B39+=+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=%28-32%29%5E2-4%2A4%2A39=400.

Discriminant d=400 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--32%2B-sqrt%28+400+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-32%29%2Bsqrt%28+400+%29%29%2F2%5C4+=+6.5
x%5B2%5D+=+%28-%28-32%29-sqrt%28+400+%29%29%2F2%5C4+=+1.5

Quadratic expression 4x%5E2%2B-32x%2B39 can be factored:
4x%5E2%2B-32x%2B39+=+4%28x-6.5%29%2A%28x-1.5%29
Again, the answer is: 6.5, 1.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-32%2Ax%2B39+%29