Answer:
x = 5
Step-by-step explanation:
Given
x = [tex]\sqrt{3x+10}[/tex] ( square both sides )
x² = 3x + 10 ( subtract 3x + 10 from both sides )
x² - 3x - 10 = 0 ← in standard form
(x - 5)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 5 = 0 ⇒ x = 5
x + 2 = 0 ⇒ x = - 2
As a check
Substitute these values into the equation and if both sides are equal then they are solutions.
x = 5
right side = [tex]\sqrt{15+10}[/tex] = [tex]\sqrt{25}[/tex] = 5 = left side ← solution
x = - 2
right side = [tex]\sqrt{-6+10}[/tex] = [tex]\sqrt{4}[/tex] = 2 ≠ - 2 ← not a solution
Thus x = 5 is the solution to the equation
