solve $x^{2}+12x = - 11$ by completing the square. which is the solution set of the equation?\n{-11…

Answer:

A. ${-11, - 1}$

Explanation:

Step1: Rewrite the equation

Given $x^{2}+12x=-11$.

Step2: Complete the square

Take half of the coefficient of $x$, square it and add to both sides. Coefficient of $x$ is $12$, half is $6$ and $6^{2} = 36$. So $x^{2}+12x + 36=-11 + 36$.

Step3: Factor the left - hand side

$(x + 6)^{2}=25$.

Step4: Take the square root of both sides

$x+6=\pm5$.

Step5: Solve for $x$

When $x + 6=5$, $x=5 - 6=-1$; when $x + 6=-5$, $x=-5 - 6=-11$. So the solution set is ${-11,-1}$.