Solve by Factoring square root of 7x+36=x+4

Problem

√(,7*x+36)=x+4

Solution

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

(√(,7*x+36))2=(x+4)2

7*x+36=x2+8*x+16

2. Rearrange the equation into standard quadratic form a*x2+b*x+c=0 by subtracting 7*x and 36 from both sides.

0=x2+8*x−7*x+16−36

x2+x−20=0

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

(x+5)*(x−4)=0

4. Apply the zero product property to find the potential solutions for x

x+5=0⇒x=−5

x−4=0⇒x=4

5. Check for extraneous solutions by substituting the values back into the original equation.
   For x=−5

√(,7*(−5)+36)=−5+4

√(,1)=−1

1≠−1

So, x=−5 is extraneous.
For x=4

√(,7*(4)+36)=4+4

√(,64)=8

8=8

Final Answer

√(,7*x+36)=x+4⇒x=4

Want more problems? Check here!