solve $x^{2}+8x = 33$ by completing the square. which is the solution set of the equation?\n{-11, 3}\n{-3…

solve $x^{2}+8x = 33$ by completing the square. which is the solution set of the equation?\n{-11, 3}\n{-3, 11}\n{-4, 4}\n{-7, 7}

solve $x^{2}+8x = 33$ by completing the square. which is the solution set of the equation?\n{-11, 3}\n{-3, 11}\n{-4, 4}\n{-7, 7}

Answer

Explanation:

Step1: Add square of half - coefficient of x

The coefficient of $x$ is $8$. Half of it is $4$, and its square is $16$. Add $16$ to both sides of the equation $x^{2}+8x = 33$. $x^{2}+8x + 16=33 + 16$

Step2: Rewrite left - hand side as perfect square

The left - hand side $x^{2}+8x + 16$ can be written as $(x + 4)^{2}$, and the right - hand side is $49$. So, $(x + 4)^{2}=49$.

Step3: Take square root of both sides

$x + 4=\pm\sqrt{49}=\pm7$.

Step4: Solve for x

When $x + 4 = 7$, $x=7 - 4=3$. When $x + 4=-7$, $x=-7 - 4=-11$.

Answer:

A. ${-11,3}$