Solve for x square root of 2x+7=x-4

Problem

√(,2*x+7)=x−4

Solution

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

√(,2*x+7)2=(x−4)2

2*x+7=x2−8*x+16

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

0=x2−8*x−2*x+16−7

x2−10*x+9=0

3. Factor the quadratic expression to find the potential values for x

(x−9)*(x−1)=0

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

x−9=0⇒x=9

x−1=0⇒x=1

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

For *x=9:√(,2*(9)+7)=9−4⇒√(,25)=5⇒5=5

For *x=1:√(,2*(1)+7)=1−4⇒√(,9)=−3⇒3≠−3

Final Answer

√(,2*x+7)=x−4⇒x=9

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