Question

What are the solutions to the quadratic equation (5y + 6)2 = 24?

y = StartFraction negative 6 + 2 StartRoot 6 EndRoot Over 5 EndFraction and y = StartFraction negative 6 minus 2 StartRoot 6 EndRoot Over 5 EndFraction
y = StartFraction negative 6 + 2 StartRoot 6 EndRoot Over 5 EndFraction and y = StartFraction 6 minus 2 StartRoot 6 EndRoot Over 5 EndFraction
y = StartFraction negative 4 StartRoot 6 EndRoot Over 5 EndFraction and y = StartFraction negative 8 StartRoot 6 EndRoot Over 5 EndFraction
y = StartFraction 4 StartRoot 6 EndRoot Over 5 EndFraction and y = StartFraction 8 StartRoot 6 EndRoot Over 5 EndFraction

Answer 1

Solve (5y + 6)^2 = 24.

Take square roots: 5y + 6 = ±√24 = ±2√6.

So 5y = -6 ± 2√6, hence y = (-6 ± 2√6)/5.

Therefore the correct choice is:
y = (-6 + 2√6)/5 and y = (-6 - 2√6)/5.