Solve. Give exact solutions.
-$$x ^ { 2 } + 8 x + 16 = 17$$
A) $\sqrt { 17 } , \sqrt { 17 }$
B) 13
C) $- 4 + \sqrt { 17 } , - 4 - \sqrt { 17 }$
D) $4 + \sqrt { 17 } , 4 - \sqrt { 17 }$

Question

Quizplus · Accepted Answer

The equation $x^2 + 8x + 16 = 17$ can be simplified to $x^2 + 8x - 1 = 0$ by subtracting 17 from both sides. Recognizing the left side as a perfect square trinomial, we can rewrite the equation as $(x + 4)^2 = 17$, which simplifies to $x + 4 = \pm\sqrt{17}$. Solving for $x$ gives $x = -4 \pm \sqrt{17}$, which matches choice C.

Solve Give Exact Solutions x2+8x+16=17x ^ { 2 } + 8 x + 16 = 17x2+8x+16=17

Solve Give Exact Solutions $x ^ { 2 } + 8 x + 16 = 17$