Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then
write and factor the trinomial.
-$$x ^ { 2 } - \frac { 2 } { 9 } x$$
A) $\frac { 1 } { 81 } ; x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 1 } { 81 } = \left( x - \frac { 1 } { 9 } \right) ^ { 2 }$
B) $\frac { 1 } { 81 } ; x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 1 } { 81 } = \left( x + \frac { 1 } { 9 } \right) ^ { 2 }$
C) $\frac { 4 } { 81 } ; x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 4 } { 81 } = \left( x - \frac { 2 } { 9 } \right) ^ { 2 }$
D) $\frac { 2 } { 81 } ; x ^ { 2 } - \frac { 2 } { 9 } x + \frac { 2 } { 81 } = \left( x - \frac { 1 } { 9 } \right) ^ { 2 }$ Solve the equation by completing the square.

Question

Quizplus · Accepted Answer

To make a perfect square trinomial, add $\left(\frac{b}{2a}\right)^2$, where $a = 1$ and $b = -\frac{2}{9}$. Thus, $\left(\frac{-\frac{2}{9}}{2}\right)^2 = \left(\frac{-1}{9}\right)^2 = \frac{1}{81}$. Factoring gives $\left(x - \frac{1}{9}\right)^2$.

Determine the Constant That Should Be Added to the Binomial x2−29xx ^ { 2 } - \frac { 2 } { 9 } xx2−92​x

Determine the Constant That Should Be Added to the Binomial $x ^ { 2 } - \frac { 2 } { 9 } x$