SOLUTION: I am having trouble with the quadratic formula: {{{x^2-2x=15x-10}}} Thank you for your time.

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Question 179457This question is from textbook
: I am having trouble with the quadratic formula:
x%5E2-2x=15x-10 Thank you for your time. This question is from textbook

Found 2 solutions by stanbon, nerdybill:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
quadratic formula:
x%5E2-2x=15x-10
------------------
Rearrange:
x^2 - 17x + 10 = 0
x = [17 +- sqrt(17^2 - 4*1*10] / 2
x = [17 +- sqrt(249)]/2
x = [17 +- 15.78..]/2
x = 16.39.. or x = 0.6101...
Cheers,
Stan H.

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-2x=15x-10
Start by moving all terms to the left:
x%5E2-2x-15x%2B10=0
x%5E2-17x%2B10=0
Since, you can't factor, you must apply the quadratic equation. Doing so yields:
x = {16.390, 0.610}
.
Details of the quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-17x%2B10+=+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=%28-17%29%5E2-4%2A1%2A10=249.

Discriminant d=249 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--17%2B-sqrt%28+249+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-17%29%2Bsqrt%28+249+%29%29%2F2%5C1+=+16.3898669190297
x%5B2%5D+=+%28-%28-17%29-sqrt%28+249+%29%29%2F2%5C1+=+0.61013308097025

Quadratic expression 1x%5E2%2B-17x%2B10 can be factored:
1x%5E2%2B-17x%2B10+=+1%28x-16.3898669190297%29%2A%28x-0.61013308097025%29
Again, the answer is: 16.3898669190297, 0.61013308097025. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-17%2Ax%2B10+%29