Solve for x square root of 15-2x=x

Problem

√(,15−2*x)=x

Solution

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

√(,15−2*x)2=x2

15−2*x=x2

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

x2+2*x−15=0

3. Factor the quadratic expression by finding two numbers that multiply to −15 and add to 2

(x+5)*(x−3)=0

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

x+5=0⇒x=−5

x−3=0⇒x=3

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

For *x=−5:√(,15−2*(−5))=√(,25)=5≠−5

For *x=3:√(,15−2*(3))=√(,9)=3=3

Final Answer

√(,15−2*x)=x⇒x=3

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