Use the quadratic formula to
-$$4 n ^ { 2 } = - 8 n - 1$$
A) $\frac { - 8 \pm \sqrt { 3 } } { 2 }$
B) $\frac { - 2 \pm \sqrt { 3 } } { 8 }$
C) $\frac { - 2 \pm \sqrt { 5 } } { 2 }$
D) $\frac { - 2 \pm \sqrt { 3 } } { 2 }$

Question

Quizplus · Accepted Answer

The quadratic formula is:$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$For the equation $4 n ^ { 2 } = - 8 n - 1$, we have:$$a = 4, b = -8, c = -1$$Substituting these values into the quadratic formula, we get:$$n = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(4)(-1)}}{2(4)}$$$$n = \frac{8 \pm \sqrt{64 + 16}}{8}$$$$n = \frac{8 \pm \sqrt{80}}{8}$$$$n = \frac{8 \pm 4\sqrt{5}}{8}$$$$n = \frac{2 \pm \sqrt{5}}{2}$$Therefore, the correct answer is D) $\frac { - 2 \pm \sqrt { 3 } } { 2 }$.

Use the Quadratic Formula to - 4n2=−8n−14 n ^ { 2 } = - 8 n - 14n2=−8n−1

Use the Quadratic Formula to
- $4 n ^ { 2 } = - 8 n - 1$