SOLUTION: Please help me solve for x: x- sqrt(2*x-1)=2

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Question 943180: Please help me solve for x: x- sqrt(2*x-1)=2
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
x- sqrt(2*x-1)=2 add sqrt(2x-1) to each side
x-sqrt(2x-1)+sqrt(2x-1)=2+sqrt(2x-1) subtract 2 from each side
x-2=sqrt(2x-1) square each side
(x-2)^2=2x-1
x%5E2-4x%2B4=2x-1 add 1 to each side
x%5E2-4x%2B5=2x subtract 2x from each side
x%5E2-6x%2B5=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B5+=+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=%28-6%29%5E2-4%2A1%2A5=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+5
x%5B2%5D+=+%28-%28-6%29-sqrt%28+16+%29%29%2F2%5C1+=+1

Quadratic expression 1x%5E2%2B-6x%2B5 can be factored:
1x%5E2%2B-6x%2B5+=+1%28x-5%29%2A%28x-1%29
Again, the answer is: 5, 1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B5+%29

ANSWERS are x=5 and x=1