Solve. Give exact solutions.
-$$x ^ { 2 } + 8 x + 16 = 24$$
A) $2 \sqrt { 6 } - 4,2 \sqrt { 6 } + 4$
B) $2 \sqrt { 6 } , - 2 \sqrt { 6 }$
C) $- 4 + 2 \sqrt { 12 } , - 4 - 2 \sqrt { 12 }$
D) $- 4 + 2 \sqrt { 6 } , - 4 - 2 \sqrt { 6 }$

Question

Quizplus · Accepted Answer

The equation is a quadratic equation that can be solved by completing the square or using the quadratic formula. The left side of the equation is a perfect square trinomial, $x^2 + 8x + 16 = (x + 4)^2$. Setting it equal to 24 and solving for $x$ gives $(x + 4)^2 = 24$, which simplifies to $x + 4 = \pm \sqrt{24}$. Further simplification leads to $x = -4 \pm 2\sqrt{6}$, which matches option D.

Solve Give Exact Solutions x2+8x+16=24x ^ { 2 } + 8 x + 16 = 24x2+8x+16=24

Solve Give Exact Solutions $x ^ { 2 } + 8 x + 16 = 24$