Answer:
x = 6
Step-by-step explanation:
Given
x - 2 = [tex]\sqrt{x+10}[/tex]
Square both sides to clear the radical
(x - 2)² = x + 10 ← expand left side using FOIL
x² - 4x + 4 = x + 10 ( subtract x + 10 from both sides )
x² - 5x - 6 = 0 ← in standard form
(x - 6)(x + 1) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 6 = 0 ⇒ x = 6
x + 1 = 0 ⇒ x = - 1
As a check
Substitute these values into the equation and if both sides are equal then they are the solutions.
x = - 1 : left side = - 1 - 2 = - 3
right side = [tex]\sqrt{-1+10}[/tex] = [tex]\sqrt{9}[/tex] = 3 ≠ - 3
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x = 6 : left side = 6 - 2 = 4
right side = [tex]\sqrt{6+10}[/tex] = [tex]\sqrt{16}[/tex] = 4
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Thus x = 6 is the solution, x = - 1 is an extraneous solution
