Answer:
x = 3
Step-by-step explanation:
Given
[tex]\sqrt{-x+4}[/tex] = x - 4 ( square both sides )
- x 4 = (x - 4)² ← expand
- x + 4 = x² - 8x + 16 ( subtract - x + 4 from both sides )
0 = x² - 7x + 12 ← in standard form
0 = (x - 3)(x - 4) ← in factored form
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x - 4 = 0 ⇒ x = 4
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions
x = 3 : [tex]\sqrt{-3+4}[/tex] = [tex]\sqrt{1}[/tex] = 1
right side = 3 - 4 = - 1
left side ≠ right side ⇒ extraneous solution
x = 4 : [tex]\sqrt{-4+4}[/tex] = 0 and right side = 4 - 4 = 0
left side = right side ⇒ x = 4 is the solution
