Solve by completing the square to obtain exact solutions.
-$$25 x ^ { 2 } + 50 x + 16 = 0$$
A) $- \frac { 2 } { 5 } , - \frac { 8 } { 5 }$
B) $- \frac { 2 } { 25 } , - \frac { 8 } { 25 }$
C) $- \frac { 8 } { 25 } , \frac { 24 } { 25 }$
D) $\frac { 2 } { 5 } , \frac { 8 } { 5 }$

Question

Quizplus · Accepted Answer

To solve $25x^2 + 50x + 16 = 0$ by completing the square, first divide the equation by 25 to simplify: $x^2 + 2x + \frac{16}{25} = 0$. Completing the square involves creating a perfect square trinomial on the left side. The equation is already in the form needed, so we find the roots directly: $x = -\frac{2}{5}$ and $x = -\frac{8}{5}$, which matches option A.

Solve by Completing the Square to Obtain Exact Solutions 25x2+50x+16=025 x ^ { 2 } + 50 x + 16 = 025x2+50x+16=0

Solve by Completing the Square to Obtain Exact Solutions $25 x ^ { 2 } + 50 x + 16 = 0$