Question

Understanding the steps to solving a quadratic equation

Answer 1

`\begin{gathered} x=-3-\sqrt[]{11} \\ x=\sqrt[]{11}-3 \end{gathered}`

Step-by-step explanation:

First we write our equation as

`\begin{gathered} 9(x^2+6x)-18=0 \\ \rightarrow9(x^2+6x)=18 \\ \rightarrow x^2+6x=(18)/(9) \end{gathered}`
`x^2+6x=2`

Now, adding 9 to both sides gives

`x^2+6x+9=2+9`

which lets us rewrite

`(x+3)^2=2+9`
`\mleft(x+3\mright)^2=11`

Taking the square root of both sides gives

`x+3=\pm\sqrt[]{11}`

Subtracting 3 from both sides gives

`x=\pm\sqrt[]{11}-3`

which gives us two solutions

`\begin{gathered} x=\sqrt[]{11}-3 \\ x=-\sqrt[]{11}-3 \end{gathered}`

which are our answers!