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

Subtract 20 from both sides

`\begin{gathered} 8x+20-20=-20\pm5√(2) \\ 8x=-20\pm5√(2) \end{gathered}`

Divide both sides by 8

`x=(-20\pm5√(2))/(8)`

So, the answer will be:

`x=(-20+5√(2))/(8);or;(-20-5√(2))/(8)`