Answer:
x = 3, x = 4
Step-by-step explanation:
Given
[tex]\sqrt{x-3}[/tex] + 3 = x ( subtract 3 from both sides )
[tex]\sqrt{x-3}[/tex] = x - 3 ( square both sides )
x - 3 = (x - 3)²
x - 3 = x² - 6x + 9 ( subtract x - 3 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 solutions
x = 3 : [tex]\sqrt{3-3}[/tex] + 3 = [tex]\sqrt{0}[/tex] + 3 = 3 = 3 = right side
x = 4 : [tex]\sqrt{4-3}[/tex] + 3 = [tex]\sqrt{1}[/tex] + 3 = 1 + 3 = 4 = right side
solutions are x = 3, x = 4
