Solve for x square root of x+30=x

Problem

√(,x+30)=x

Solution

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

√(,x+30)2=x2

x+30=x2

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

0=x2−x−30

3. Factor the quadratic expression by finding two numbers that multiply to −30 and add to −1

0=(x−6)*(x+5)

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

x−6=0⇒x=6

x+5=0⇒x=−5

5. Check for extraneous solutions by substituting the values back into the original equation.
   For x=6 √(,6+30)=√(,36)=6 This is true.
   For x=−5 √(,−5+30)=√(,25)=5 but the right side is −5 Since 5≠−5 x=−5 is extraneous.

Final Answer

√(,x+30)=x⇒x=6

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