Solve for x square root of x+20=x

Problem

√(,x+20)=x

Solution

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

√(,x+20)2=x2

x+20=x2

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

0=x2−x−20

3. Factor the quadratic expression by finding two numbers that multiply to −20 and add to −1

0=(x−5)*(x+4)

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

x−5=0⇒x=5

x+4=0⇒x=−4

5. Check for extraneous solutions by substituting the values back into the original equation √(,x+20)=x
   For x=5 √(,5+20)=√(,25)=5 This is true.
   For x=−4 √(,−4+20)=√(,16)=4 but the right side is −4 Since 4≠−4 this solution is extraneous.

Final Answer

x=5

Want more problems? Check here!