SOLUTION: How do you solve the equation (x-1)^2=4 eight different ways and what methods are used?

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Question 309223: How do you solve the equation (x-1)^2=4 eight different ways and what methods are used?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
(x-1)^2=4
#1
take square roots
x-1=+-2
x-1=2
x=3
x-1=-2
x=-1
x=(-1,3)
#2
(x-1)*(x-1)=4
x^2-2x+1=4
x^2-2x-3=0
(x-3)*(x+1)=0
x=(-1,3)
#3
use quadratic formula
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%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=%28-2%29%5E2-4%2A1%2A-3=16.

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

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+3
x%5B2%5D+=+%28-%28-2%29-sqrt%28+16+%29%29%2F2%5C1+=+-1

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

#4 graph
Good luck on the other 4 ways