Solve the equation by using the quadratic formula. $$7 x ( x - 2 ) = 5$$
A) $\left\{ 1 \pm \frac { 2 \sqrt { 21 } } { 7 } i \right\}$
B) $\left\{ 1 \pm \frac { 2 \sqrt { 21 } } { 7 } \right\}$
C) $\left\{ - 1 + \frac { 2 \sqrt { 21 } } { 7 } i , - 6 + \frac { 2 \sqrt { 21 } } { 7 } i \right\}$
D) $\left\{ - 1 + \frac { 2 \sqrt { 21 } } { 7 } , - 6 + \frac { 2 \sqrt { 21 } } { 7 } \right\}$

Question

Quizplus · Accepted Answer

First, expand and rearrange the equation into standard form: $7x^2 - 14x - 5 = 0$. Applying the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, with $a = 7$, $b = -14$, and $c = -5$, yields $x = \frac{14 \pm \sqrt{196 + 140}}{14} = \frac{14 \pm \sqrt{336}}{14} = 1 \pm \frac{2\sqrt{21}}{7}$.

Solve the Equation by Using the Quadratic Formula 7x(x−2)=57 x ( x - 2 ) = 57x(x−2)=5

Solve the Equation by Using the Quadratic Formula $7 x ( x - 2 ) = 5$