Question

What is the solution to x = square root 3x + 10?

Answer 1

Answer:

x = 5

Step-by-step explanation:

Given

x = $\sqrt{3x+10}$ ( 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 = $\sqrt{15+10}$ = $\sqrt{25}$ = 5 = left side ← solution

x = - 2

right side = $\sqrt{-6+10}$ = $\sqrt{4}$ = 2 ≠ - 2 ← not a solution

Thus x = 5 is the solution to the equation