Solve the equation by completing the square.
-$$a ^ { 2 } + 14 a + 45 = 0$$
A) $- 5 , - 9$
B) $54 , - 9$
C) 5,9
D) $\sqrt { 45 } , - \sqrt { 45 }$

Question

Quizplus · Accepted Answer

To solve the equation $a^2 + 14a + 45 = 0$ by completing the square, we first move the constant term to the other side: $a^2 + 14a = -45$. Then, we add $(\frac{14}{2})^2 = 49$ to both sides to complete the square: $a^2 + 14a + 49 = 4$, which simplifies to $(a + 7)^2 = 4$. Taking the square root of both sides gives $a + 7 = \pm 2$, leading to $a = -7 \pm 2$, which results in $a = -5$ and $a = -9$.

Solve the Equation by Completing the Square a2+14a+45=0a ^ { 2 } + 14 a + 45 = 0a2+14a+45=0

Solve the Equation by Completing the Square $a ^ { 2 } + 14 a + 45 = 0$