Question

Solve the quadratic equation by the square root method and write the solutions in radical forms simplify the solutions

Answer 1

Given the following quadratic equation:

$(8x+20)^2=50$

We will solve the equation by the square root method.

Taking the square root of both sides:

$\begin{gathered} \sqrt{(8x+20)^2}=\pm\sqrt{50} \\ \\ 8x+20=\pm\sqrt{50} \\ Note:\sqrt{50}=\sqrt{25*2}=5\sqrt{2} \\ \\ 8x+20=\pm5\sqrt{2} \end{gathered}$

Subtract 20 from both sides

$\begin{gathered} 8x+20-20=-20\pm5\sqrt{2} \\ 8x=-20\pm5\sqrt{2} \end{gathered}$

Divide both sides by 8

$x=\frac{-20\pm5\sqrt{2}}{8}$

So, the answer will be:

$x=\frac{-20+5\sqrt{2}}{8};or;\frac{-20-5\sqrt{2}}{8}$