Solve by completing the square.
-$$\mathrm { q } ^ { 2 } + 8 \mathrm { q } - 3 = 0$$
A) $4 + \sqrt { 19 }$
B) $- 4 \pm \sqrt { 19 }$
C) $- 4 \pm 2 \sqrt { 19 }$
D) $- 1 \pm \sqrt { 19 }$

Question

Quizplus · Accepted Answer

To solve the quadratic equation $q^2 + 8q - 3 = 0$ by completing the square, we first move the constant term to the right side: $q^2 + 8q = 3$. Then, we add $(\frac{8}{2})^2 = 16$ to both sides to complete the square: $q^2 + 8q + 16 = 19$, which simplifies to $(q + 4)^2 = 19$. Taking the square root of both sides gives $q + 4 = \pm \sqrt{19}$, so $q = -4 \pm \sqrt{19}$.

Solve by Completing the Square q2+8q−3=0\mathrm { q } ^ { 2 } + 8 \mathrm { q } - 3 = 0q2+8q−3=0

Solve by Completing the Square $\mathrm { q } ^ { 2 } + 8 \mathrm { q } - 3 = 0$