Solve the equation by completing the square.
-$$9 x ^ { 2 } + 36 x + 20 = 0$$
A) $\left\{ \frac { 2 } { 3 } , \frac { 10 } { 3 } \right\}$
B) $\left\{ - \frac { 10 } { 3 } , \frac { 10 } { 3 } \right\}$
C) $\left\{ - \frac { 2 } { 3 } , - \frac { 10 } { 3 } \right\}$
D) $\left\{ - \frac { 2 } { 9 } , - \frac { 10 } { 9 } \right\}$

Question

Quizplus · Accepted Answer

To solve the equation $9x^2 + 36x + 20 = 0$ by completing the square, first divide the entire equation by 9 to simplify: $x^2 + 4x + \frac{20}{9} = 0$. Completing the square involves creating a perfect square trinomial on the left side of the equation. To do this, add and subtract $(\frac{4}{2})^2 = 4$ inside the equation, leading to $x^2 + 4x + 4 - 4 + \frac{20}{9} = 0$, which simplifies to $(x + 2)^2 = \frac{16}{9}$. Taking the square root of both sides gives $x + 2 = \pm\frac{4}{3}$, leading to $x = -2 \pm \frac{4}{3}$, which simplifies to the solutions $x = -\frac{2}{3}$ and $x = -\frac{10}{3}$.

Solve the Equation by Completing the Square 9x2+36x+20=09 x ^ { 2 } + 36 x + 20 = 09x2+36x+20=0

Solve the Equation by Completing the Square $9 x ^ { 2 } + 36 x + 20 = 0$