what are the solutions to the quadratic equation (5y + 6)^2 = 24?\no y = \\frac{-6 + 2\\sqrt{6}}{5} and y =…

what are the solutions to the quadratic equation (5y + 6)^2 = 24?\no y = \\frac{-6 + 2\\sqrt{6}}{5} and y = \\frac{-6 - 2\\sqrt{6}}{5}\no y = \\frac{-6 + 2\\sqrt{6}}{5} and y = \\frac{6 - 2\\sqrt{6}}{5}\no y = \\frac{-4\\sqrt{6}}{5} and y = \\frac{-8\\sqrt{6}}{5}\no y = \\frac{4\\sqrt{6}}{5} and y = \\frac{8\\sqrt{6}}{5}

what are the solutions to the quadratic equation (5y + 6)^2 = 24?\no y = \\frac{-6 + 2\\sqrt{6}}{5} and y = \\frac{-6 - 2\\sqrt{6}}{5}\no y = \\frac{-6 + 2\\sqrt{6}}{5} and y = \\frac{6 - 2\\sqrt{6}}{5}\no y = \\frac{-4\\sqrt{6}}{5} and y = \\frac{-8\\sqrt{6}}{5}\no y = \\frac{4\\sqrt{6}}{5} and y = \\frac{8\\sqrt{6}}{5}

Answer

Explanation:

Step1: Take square - root of both sides

[5y + 6=\pm\sqrt{24}] Since (\sqrt{24}=\sqrt{4\times6}=2\sqrt{6}), we have (5y + 6=\pm2\sqrt{6}).

Step2: Solve for (y) when (5y + 6 = 2\sqrt{6})

Subtract 6 from both sides: (5y=2\sqrt{6}-6). Then (y=\frac{-6 + 2\sqrt{6}}{5}).

Step3: Solve for (y) when (5y + 6=-2\sqrt{6})

Subtract 6 from both sides: (5y=-2\sqrt{6}-6). Then (y=\frac{-6-2\sqrt{6}}{5}).

Answer:

A. (y=\frac{-6 + 2\sqrt{6}}{5}) and (y=\frac{-6-2\sqrt{6}}{5})