SOLUTION: Solve (2x - 1)^2 = 20 Show every step

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Question 295760: Solve (2x - 1)^2 = 20 Show every step
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
%282x-1%29%5E2=20 show full problem
%282x-1%29%282x-1%29=20foil
4x%5E2-2x-2x%2B1=20 add like terms
4x%5E2-4x%2B1=20 subtract 20
4x%5E2-4x-19=0
use quadratic formula
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-4x%2B-19+=+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=%28-4%29%5E2-4%2A4%2A-19=320.

Discriminant d=320 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+320+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+320+%29%29%2F2%5C4+=+2.73606797749979
x%5B2%5D+=+%28-%28-4%29-sqrt%28+320+%29%29%2F2%5C4+=+-1.73606797749979

Quadratic expression 4x%5E2%2B-4x%2B-19 can be factored:
4x%5E2%2B-4x%2B-19+=+4%28x-2.73606797749979%29%2A%28x--1.73606797749979%29
Again, the answer is: 2.73606797749979, -1.73606797749979. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-4%2Ax%2B-19+%29