Best explained and correct answer gets brainliest.

To get rid of the square root, square both terms.





Move all the terms to the left of equal with changed sign



Sum like terms.



Multiply all the terms for -1 (change their sign) to make the x positive



We have a second grade equation, that we'll solve in this way.

x₁,₂ = (-b±√Δ)/2a

Δ = b²-4ac

You call a (1)x², you call b 9 and you call c 14

x1,2 = (-(-9)±√(-9)² - 4*1*14)/2*1

x1,2 = (9±√81-56)/2

x1,2 = (9±√25)/2

x1,2 = (9±5)/2

x1 = (9+5)/2 = 14/2 = 7

x2 = (9-5)/2 = 4/2 = 2

Check what x is true for √x+2 = x-4

√7+2 = 7-4

√9 = 3

3 = 3 (true)

√2+2 = 2-4

√4 = -2

2 = -2 (not true)

Therefore the only solution is x = 7

Answer C