Question

Solve for x. Enter the solutions from least to greatest.Round to two decimal places.(x+3)^2 – 3 = 0lesser x =greater x =

Answer 1

The given equation is

`\mleft(x+3\mright)^2-3=0`

Simplify the equation by adding 3 to both sides of the equation

`\mleft(x+3\mright)^2-3+3=3`

This is simplified to give

`\mleft(x+3\mright)^2=3`

This can be further simplified as follows

`\begin{gathered} x+3=\pm\sqrt[]{3} \\ x=\pm\sqrt[]{3}-3 \end{gathered}`

Hence, the solution is

`\begin{gathered} x=-\sqrt[]{3}-3,x=\sqrt[]{3}-3 \\ \Rightarrow x=-1.73-3,x=1.73-3 \\ x=-4.73,x=1.27 \end{gathered}`

Therefore, the solution is

Lesser x = - 4.73

Greater x = 1.27