SOLUTION: x^2-16x+4=0

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Question 357185: x^2-16x+4=0
Found 2 solutions by stanbon, nerdybill:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-16x+4=0
Quadratic Formula:
x = [16 +- sqrt(16^2-4*4)]/2
---
x = [16 +- sqrt(240)]/2
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x = [16 +- 4sqrt(15)]/2
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x = [8 +- 2sqrt(15)]
===========================
Cheers,
Stan H.

Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
x^2-16x+4=0
.
Since you can't factor, you must apply the quadratic formula. Doing so yields:
x = {15.75, 0.25}
.
Details of quadratic follows:
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-16x%2B4+=+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=%28-16%29%5E2-4%2A1%2A4=240.

Discriminant d=240 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--16%2B-sqrt%28+240+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-16%29%2Bsqrt%28+240+%29%29%2F2%5C1+=+15.7459666924148
x%5B2%5D+=+%28-%28-16%29-sqrt%28+240+%29%29%2F2%5C1+=+0.254033307585166

Quadratic expression 1x%5E2%2B-16x%2B4 can be factored:
1x%5E2%2B-16x%2B4+=+1%28x-15.7459666924148%29%2A%28x-0.254033307585166%29
Again, the answer is: 15.7459666924148, 0.254033307585166. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-16%2Ax%2B4+%29