Question

Which of the following are solutions to the equation below?Check all that apply(5x - 2)2 = 10O A. x=4126O B, *= -10 + 25C. x = V0 + 25o D. x = 125E. x= 12 + 2O F. *=-+ 2What are the following are solutions to the equation ?

Answer 1

The question given is to solve:

`(5x-2)^2=10`

This is a quadratic equation and in order to solve it, all we need to do is to find the square root of both sides and solve the remaining expression algebraically to find x.

First let us find the square root:

`\begin{gathered} (5x-2)^2=10 \\ \text{ Square root both sides} \\ \sqrt[]{(5x-2)^2}=\sqrt[]{10} \\ \\ 5x-2=\sqrt[]{10} \\ \end{gathered}`

Now we can simply add 2 to both sides after which we divide both sides by 5.

`\begin{gathered} 5x-2=\sqrt[]{10} \\ \text{add 2 to both sides} \\ 5x-2+2=\sqrt[]{10}+2 \\ 5x=\sqrt[]{10}+2 \\ \text{divide both sides by 5} \\ (5x)/(5)=\frac{\sqrt[]{10}+2}{5} \\ \\ \therefore x=\frac{\pm\sqrt[]{10}+2}{5} \end{gathered}`

Hence we have two answers, these are:

`\begin{gathered} x=\frac{\sqrt[]{10}+2}{5}\text{ (Option C)} \\ OR \\ x=\frac{-\sqrt[]{10}+2}{5}\text{ (Option B)} \end{gathered}`