Question

What is the solution to the equation squareroot 5xsquared +2x -25 = squareroot x+5? Assume the range is all real numbers.
x = –6
x = 5
x = 6, x = –5
x = –6, x = 5

Answer 1

Solve sqrt(5x^2 + 2x − 25) = sqrt(x + 5).

Both square roots require x + 5 ≥ 0 ⇒ x ≥ −5. Square both sides:
5x^2 + 2x − 25 = x + 5
⇒ 5x^2 + x − 30 = 0.

Solve the quadratic:
x = [−1 ± sqrt(1 + 600)]/10 = [−1 ± sqrt(601)]/10.

So the exact solutions are x = (−1 + sqrt(601))/10 ≈ 2.35153 and x = (−1 − sqrt(601))/10 ≈ −2.55153. Both lie in the domain x ≥ −5, so both are valid.

None of the multiple-choice options given (−6, 5, 6 and −5, etc.) are correct.