Answer:
x = 1
Step-by-step explanation:
Given
x + 2[tex]\sqrt{x}[/tex] - 3 = 0 ( subtract x - 3 from both sides )
2[tex]\sqrt{x}[/tex] = 3 - x ( square both sides )
4x = (3 - x)² ← expand using FOIL
4x = 9 - 6x + x² ( subtract 4x from both sides )
0 = x² - 10x + 9 ← in standard form
0 = (x - 1)(x - 9) ← in factored form
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 9 = 0 ⇒ x = 9
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are solutions.
x = 1 : 1 + 2[tex]\sqrt{1}[/tex] - 3 = 1 + 2 - 3 = 0 → x = 1 is a solution
x = 9 : 9 + 2[tex]\sqrt{9}[/tex] - 3 = 9 + 6 - 3 = 12 ≠ 0
x = 9 is an extraneous solution while x = 1 is a solution
