Question

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

Answer 1

The value of y is, $y=\frac{2\sqrt{6}-6}{5},\:y=\frac{-2\sqrt{6}-6}{5}$

We have given that,

$\left(5y+6\right)^2=24$

We have to determine the value of y,

What is the formula for the quadratic equation?

$\mathrm{For\:}\left(g\left(x\right)\right)^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}$

Therefore,we get

$5y+6=\sqrt{24}$

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

$\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}$

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

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

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

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

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

Therefore the value of y is,

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

To learn more about the quadratic equation visit:

brainly.com/question/1214333

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