Answer:
x = 4
Step-by-step explanation:
given
[tex]\sqrt{x+12}[/tex] = x ( square both sides )
([tex]\sqrt{x+12}[/tex])² = x²
x + 12 = x² ( subtract x + 12 from both sides )
x² - x - 12 = 0 ← in standard form
(x - 4)(x + 3) = 0
equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 3 = 0 ⇒ x = - 3
As a check
substitute these values into the equation and if the left side equals the right side then they are the solutions
x = 4 : [tex]\sqrt{12+4}[/tex] = [tex]\sqrt{16}[/tex] = 4 = right side
x = - 3 : [tex]\sqrt{-3+12}[/tex] = [tex]\sqrt{9}[/tex] = 3 ≠ - 3
The only valid solution is x = 4
