Solve by completing the square to obtain exact solutions.
-$$9 x ^ { 2 } + 27 x + 20 = 0$$
A) $- \frac { 3 } { 4 } , - \frac { 5 } { 3 }$
B) $- \frac { 4 } { 3 } , - \frac { 5 } { 3 }$
C) $\frac { 4 } { 3 } , \frac { 5 } { 3 }$
D) $\frac { 3 } { 4 } , \frac { 3 } { 5 }$

Question

Quizplus · Accepted Answer

To solve $9x^2 + 27x + 20 = 0$ by completing the square, first divide the equation by 9 to simplify: $x^2 + 3x + \frac{20}{9} = 0$. To complete the square, we need to add and subtract $\left(\frac{3}{2}\right)^2 = \frac{9}{4}$ inside the equation, leading to $x^2 + 3x + \frac{9}{4} - \frac{9}{4} + \frac{20}{9} = 0$, which simplifies to $\left(x + \frac{3}{2}\right)^2 = \frac{9}{4} - \frac{20}{9}$. Solving for $x$ gives the roots $-\frac{4}{3}$ and $-\frac{5}{3}$.

Solve by Completing the Square to Obtain Exact Solutions 9x2+27x+20=09 x ^ { 2 } + 27 x + 20 = 09x2+27x+20=0

Solve by Completing the Square to Obtain Exact Solutions $9 x ^ { 2 } + 27 x + 20 = 0$