Question

Solve (u + 4) ^ 2 - 4 = 0 , where u is a real number. Simplify your answer as much as possible . If there is more than one solution, separate them with commas. If there is no solution, click "No solution."

Answer 1

The given equation is:

`(u+4)^2-4=0`

By transferring '-4' to the R.H.S of the equation, we have:

`\begin{gathered} (u+4)^2=0+4 \\ (u+4)^2=4 \end{gathered}`

By taking the square root of both sides, we have:

`\begin{gathered} \sqrt[]{(u+4)^2}=\sqrt[]{4} \\ \end{gathered}`

Thus, we have:

`\begin{gathered} u+4=\pm2 \\ u=\pm2-4 \end{gathered}`

This implies that:

`\begin{gathered} u=-2-4\text{ OR +2-4} \\ u=-6\text{ OR -2} \end{gathered}`

Hence, it has more than one solution and they are -6 and -2