Solve for x square root of 8-2x=x

Problem

√(,8−2*x)=x

Solution

1. Square both sides of the equation to eliminate the radical.

√(,8−2*x)2=x2

8−2*x=x2

2. Rearrange the equation into a standard quadratic form a*x2+b*x+c=0 by moving all terms to one side.

0=x2+2*x−8

3. Factor the quadratic expression by finding two numbers that multiply to −8 and add to 2

0=(x+4)*(x−2)

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

x+4=0⇒x=−4

x−2=0⇒x=2

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

For *x=−4:√(,8−2*(−4))=√(,16)=4≠−4

For *x=2:√(,8−2*(2))=√(,4)=2=2

Final Answer

√(,8−2*x)=x⇒x=2

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