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

Answer:

there are two solutions:

a) $y=\frac{-6+2\sqrt{6} }{5}$, and

b) $y=\frac{-6-2\sqrt{6} }{5}$

Step-by-step explanation:

In the equation: $(5y+6)^2=24$, since a perfect square with the unknown "y" is isolated on the left of the equal sign, we start by applying the square root on both sides of the equality, and then on isolating the unknown:

$(5y+6)^2=24\\\sqrt{(5y+6)^2} =+/-\sqrt{24} \\(5y+6)=+/-\sqrt{6*4} \\(5y+6)=+/-2\sqrt{6}\\5y=-6+/-2\sqrt{6}\\y=\frac{-6+/-2\sqrt{6} }{5}$

Therefore there are two solutions:

a) $y=\frac{-6+2\sqrt{6} }{5}$, and

b) $y=\frac{-6-2\sqrt{6} }{5}$

Answer 2

Answer: A

$y=\frac{-6+2\sqrt{6} }{5} \\y=\frac{-6-2\sqrt{6} }{5}$

Step-by-step explanation:

just did this