Solve for x square root of 2x+12=x-6

Problem

√(,2*x+12)=x−6

Solution

1. Square both sides of the equation to eliminate the radical on the left side.

√(,2*x+12)2=(x−6)2

2*x+12=x2−12*x+36

2. Rearrange the equation into standard quadratic form by moving all terms to one side.

0=x2−12*x−2*x+36−12

x2−14*x+24=0

3. Factor the quadratic expression by finding two numbers that multiply to 24 and add to −14

(x−12)*(x−2)=0

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

x−12=0⇒x=12

x−2=0⇒x=2

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

For *x=12:√(,2*(12)+12)=12−6⇒√(,36)=6⇒6=6

For *x=2:√(,2*(2)+12)=2−6⇒√(,16)=−4⇒4≠−4

Final Answer

x=12

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