Solve the equation by completing the square.
-$$4 \mathrm {~d} ^ { 2 } + 16 \mathrm {~d} + 15 = 0$$
A) $- \frac { 5 } { 2 } , - \frac { 3 } { 2 }$
B) $- \frac { 2 } { 5 } , - \frac { 3 } { 2 }$
C) $\frac { 5 } { 2 } , \frac { 3 } { 2 }$
D) $\frac { 2 } { 5 } , \frac { 2 } { 3 }$

Question

Quizplus · Accepted Answer

To solve $4d^2 + 16d + 15 = 0$ by completing the square, first divide the equation by 4 to simplify: $d^2 + 4d + \frac{15}{4} = 0$. Then, find the value to complete the square: $(4/2)^2 = 4$. Subtract and add $4$ inside the equation, leading to $d^2 + 4d + 4 - 4 + \frac{15}{4} = 0$, which simplifies to $(d + 2)^2 = \frac{1}{4}$. Solving for $d$ gives $d + 2 = \pm \frac{1}{2}$, resulting in $d = -\frac{5}{2}$ and $d = -\frac{3}{2}$.

Solve the Equation by Completing the Square 4 d2+16 d+15=04 \mathrm {~d} ^ { 2 } + 16 \mathrm {~d} + 15 = 04 d2+16 d+15=0

Solve the Equation by Completing the Square $4 \mathrm {~d} ^ { 2 } + 16 \mathrm {~d} + 15 = 0$