SOLUTION: Can you please show me the steps of how to solve this equation using the Square Root Property m^2 = 8m + 3

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Question 170113: Can you please show me the steps of how to solve this equation using the Square Root Property
m^2 = 8m + 3
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
m^2 = 8m + 3
m^2 - 8m - 3 = 0
That can't be factored, so use the quadratic formula.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-8x%2B-3+=+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=%28-8%29%5E2-4%2A1%2A-3=76.

Discriminant d=76 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+76+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+76+%29%29%2F2%5C1+=+8.35889894354067
x%5B2%5D+=+%28-%28-8%29-sqrt%28+76+%29%29%2F2%5C1+=+-0.358898943540674

Quadratic expression 1x%5E2%2B-8x%2B-3 can be factored:
1x%5E2%2B-8x%2B-3+=+%28x-8.35889894354067%29%2A%28x--0.358898943540674%29
Again, the answer is: 8.35889894354067, -0.358898943540674. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B-3+%29

The solver defaults to x. Replace that with m.
m = (+8 +- sqrt(64 + 12))/2
m = 4 + sqrt(19)
m = 4 - sqrt(19)