Question

Solve x= √x+7 +5
check for extraneous solutions

(pls show work)

Answer 1

x = 9

Explanation:

Let's solve your equation step-by-step.

`x=√(x+7) +5`

Step 1: Flip the equation.

`√(x+7) +5=x`

Step 2: Add -5 to both sides.

`√(x+7) +5-5=x-5`

Step 3: Solve Square Root.

`√(x+7) =x-5`

`{x+7} =(x-5)^2` (Square both sides)

`x+7=x^2-10x+25`

`-x^2+11x-18=0`

`(-x+2)(x-9)=0` (Factor left side of equation)

`-x+2=0` or
`x-9=0` (Set factors equal to 0)

x = 2 or x = 9

x = 2 (Doesn't work on the original equation)

x = 9 (Works in the original equation)

Answer:

x = 9