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Understanding the steps to solving a quadratic equation

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Answer:


\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!

User Kshitij Aggarwal
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