Solve the quadratic equation by completing the square and applying the square root property. $$( 3 w + 2 ) ( w - 1 ) = 5$$
A) $\left\{ \frac { 1 } { 6 } - \frac { \sqrt { 83 } } { 6 } , \frac { 1 } { 6 } + \frac { \sqrt { \sqrt { 83 } } } { 6 } \right\}$
B) $\left\{ \frac { 1 } { 6 } - \frac { i \sqrt { 83 } } { 6 } , \frac { 1 } { 6 } + \frac { i \sqrt { \sqrt { 83 } } } { 6 } \right\}$
C) $\left\{ \frac { 1 } { 6 } - \frac { \sqrt { 85 } } { 6 } , \frac { 1 } { 6 } + \frac { \sqrt { 85 } } { 6 } \right\}$
D) $\left\{ - \frac { 2 } { 3 } , 1 \right\}$

Question

Quizplus · Accepted Answer

First, expand and simplify the given equation: $3w^2 + 2w - w - 2 = 5$, which simplifies to $3w^2 + w - 7 = 0$. Completing the square involves rearranging the equation to the form $(w + \frac{b}{2a})^2 = \frac{c}{a} + (\frac{b}{2a})^2$, where $a = 3$, $b = 1$, and $c = -7$. After completing the square, we find the equation in the form $(w + \frac{1}{6})^2 = \frac{85}{36}$, leading to solutions $w = \frac{1}{6} \pm \frac{\sqrt{85}}{6}$.

Solve the Quadratic Equation by Completing the Square and Applying (3w+2)(w−1)=5( 3 w + 2 ) ( w - 1 ) = 5(3w+2)(w−1)=5

Solve the Quadratic Equation by Completing the Square and Applying $( 3 w + 2 ) ( w - 1 ) = 5$