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

Question 943180: Please help me solve for x: x- sqrt(2*x-1)=2
Answer by macston(5194) (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
add 1 to each side
subtract 2x from each side

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=16 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 5, 1. Here's your graph:

ANSWERS are x=5 and x=1

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