SOLUTION: Solve for x: 5(x – 2^)2 = 3

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Question 683900: Solve for x: 5(x – 2^)2 = 3
Answer by jerryguo41(197) About Me  (Show Source):
You can put this solution on YOUR website!
5(x–2)^2=3
Expand
5%28x%5E2-4x%2B4%29=3
Distribute
5x%5E2-20x%2B20=3
Subtract
5x%5E2-20x%2B17=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-20x%2B17+=+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=%28-20%29%5E2-4%2A5%2A17=60.

Discriminant d=60 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--20%2B-sqrt%28+60+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-20%29%2Bsqrt%28+60+%29%29%2F2%5C5+=+2.77459666924148
x%5B2%5D+=+%28-%28-20%29-sqrt%28+60+%29%29%2F2%5C5+=+1.22540333075852

Quadratic expression 5x%5E2%2B-20x%2B17 can be factored:
5x%5E2%2B-20x%2B17+=+5%28x-2.77459666924148%29%2A%28x-1.22540333075852%29
Again, the answer is: 2.77459666924148, 1.22540333075852. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-20%2Ax%2B17+%29

Simplify
%2820%2B-sqrt%2860%29%29%2F10
==>
%2810%2B-sqrt%2815%29%29%2F5
Thus
x= %2810%2B-sqrt%2815%29%29%2F5 or 2.77,1.22