Solve for x square root of 2x+1+1=x

Problem

√(,2*x+1)+1=x

Solution

1. Isolate the radical term by subtracting 1 from both sides of the equation.

√(,2*x+1)=x−1

2. Square both sides of the equation to eliminate the square root.

(√(,2*x+1))2=(x−1)2

3. Expand the squared expressions on both sides.

2*x+1=x2−2*x+1

4. Rearrange the equation into standard quadratic form by subtracting 2*x and 1 from both sides.

0=x2−4*x

5. Factor the quadratic expression by taking out the greatest common factor.

0=x*(x−4)

6. Solve for x by setting each factor equal to zero.

x=0

x=4

7. Check for extraneous solutions by substituting the values back into the original equation.

For *x=0:√(,2*(0)+1)+1=√(,1)+1=2≠0

For *x=4:√(,2*(4)+1)+1=√(,9)+1=3+1=4

Final Answer

√(,2*x+1)+1=x⇒x=4

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