Solve the quadratic equation by completing the square and applying the square root property.
-$$n ^ { 2 } + 18 n = - 75$$
A) $\{ - 9 - \sqrt { 6 } , - 9 + \sqrt { 6 } \}$
B) $\{ 9 - \sqrt { 6 } , 9 + \sqrt { 6 } \}$
C) $\{ - 9 - \sqrt { 249 } , - 9 + \sqrt { 249 } \}$
D)
$\left\{ \frac { - 18 - \sqrt { 249 } } { 2 } , \frac { - 18 + \sqrt { 249 } } { 2 } \right\}$

Question

Quizplus · Accepted Answer

To solve the quadratic equation $n^2 + 18n = -75$ by completing the square, first move all terms to one side to set the equation to 0: $n^2 + 18n + 75 = 0$. To complete the square, add $\left(\frac{18}{2}\right)^2 = 81$ to both sides, resulting in $n^2 + 18n + 81 = 81 - 75$, which simplifies to $n^2 + 18n + 81 = 6$. This can be written as $(n + 9)^2 = 6$. Taking the square root of both sides gives $n + 9 = \pm \sqrt{6}$, leading to the solutions $n = -9 \pm \sqrt{6}$.

Solve the Quadratic Equation by Completing the Square and Applying n2+18n=−75n ^ { 2 } + 18 n = - 75n2+18n=−75

Solve the Quadratic Equation by Completing the Square and Applying $n ^ { 2 } + 18 n = - 75$