Question

Complete the square -2x^2-12x-9=0

Answer 1

Given the Quadratic Equation:

$-2x^2-12x-9=0$

You need to follow these steps in order to complete the square:

1. You can identify that the equation has this form:

$ax^2+bx+c=0$

And, in this case:

$a=-2$

Since you need that:

$a=1$

You need to divide both sides of the equation by -2:

$\begin{gathered} -\frac{2x^2}{(-2)}-\frac{12x}{(-2)}-\frac{9}{(-2)}=\frac{0}{(-2)} \\ \\ x^2+6x+\frac{9}{2}=0 \end{gathered}$

2. Subtract the Constant Term from both sides of the equation:

$\begin{gathered} x^2+6x+\frac{9}{2}-(\frac{9}{2})=0-(\frac{9}{2}) \\ \\ x^2+6x=-\frac{9}{2} \end{gathered}$

3. Notice that:

$b=6$

You need to add the following value to both sides of the equation:

$(\frac{b}{2})^2=(\frac{6}{2})^2=3^2$

Then:

$\begin{gathered} x^2+6x+3^2=-\frac{9}{2}+3^2 \\ \\ x^2+6x+3^2=-\frac{9}{2}+9 \\ \\ x^2+6x+3^2=\frac{9}{2} \end{gathered}$

4. Rewrite the Perfect Square on the left side of the equation:

$(x+3)^2=\frac{9}{2}$

Hence, the answer is:

$(x+3)^2=\frac{9}{2}$