Question

Which of the following correctly completes the square for the equationbelow?X? + 18x = 0A. (x + 18)2 = 81B. (x + 9)2 = 87C. (x + 3)2 = 9OD. (3)

Answer 1

The condition for the perfect square of a quadratic equation is given as:

`b^2-4ac=0`

From the question;

`\begin{gathered} x^2+18x=0 \\ a=1,\text{ b=18, c=?} \\ \end{gathered}`

To obtain c, we have;

`\begin{gathered} b^2-4ac=0 \\ 18^2-4(1)c=0 \\ 324-4c=0 \\ 4c=324 \\ c=(324)/(4) \\ c=81 \end{gathered}`

The complete version of the equation becomes:

`\begin{gathered} x^2+18x+81=0 \\ (x+9)^2=0 \end{gathered}`

Hence, the correct option is Option B