The equation 5x = √(10 + 15x) is solved by squaring both sides to remove the square root, leading to a quadratic equation, which when solved using the quadratic formula gives the solution x = -2/5, making the correct answer D. -2/5.
The solution to the equation 5x = √(10 + 15x) is determined by squaring both sides of the equation to eliminate the square root and then solving the resulting quadratic equation. First, we square both sides:
(5x)² = (10 + 15x)
Then, we get:
25x² = 10 + 15x
To find the values of x, you move all the terms to one side:
25x² - 15x - 10 = 0
And utilizing the quadratic formula, we can find the possible values for x. After computation, we conclude that the solution is x = -2/5. Hence, the correct answer is D. -2/5.