28 solve $x^{2}+8x = 33$ for $x$ by completing the square.

Explanation:

Step1: Add square of half - coefficient of x to both sides

The coefficient of $x$ is $8$. Half of it is $4$ and its square is $16$. $x^{2}+8x + 16=33 + 16$

Step2: Rewrite left - hand side as a perfect square

$(x + 4)^{2}=49$

Step3: Take square root of both sides

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

Step4: Solve for x

$x=-4\pm7$ When we take the plus sign: $x=-4 + 7=3$ When we take the minus sign: $x=-4-7=-11$

Answer:

$x = 3$ or $x=-11$