Solve the equation by the method of your choice.
-$$2 x ^ { 2 } + 10 x = - 5$$
A) $\left\{ \frac { - 5 - \sqrt { 15 } } { 2 } , \frac { - 5 + \sqrt { 15 } } { 2 } \right\}$
B) $\left\{ \frac { - 5 - \sqrt { 35 } } { 2 } , \frac { - 5 + \sqrt { 35 } } { 2 } \right\}$
C) $\left\{ \frac { - 10 - \sqrt { 15 } } { 2 } , \frac { - 10 + \sqrt { 15 } } { 2 } \right\}$
D) $\left\{ \frac { - 5 - \sqrt { 15 } } { 4 } , \frac { - 5 + \sqrt { 15 } } { 4 } \right\}$

Question

Quizplus · Accepted Answer

First, rearrange the equation to standard form: $2x^2 + 10x + 5 = 0$. Then, use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with $a = 2$, $b = 10$, and $c = 5$. This gives $x = \frac{-10 \pm \sqrt{100 - 40}}{4} = \frac{-10 \pm \sqrt{60}}{4}$, which simplifies to $x = \frac{-5 \pm \sqrt{15}}{2}$.

Solve the Equation by the Method of Your Choice 2x2+10x=−52 x ^ { 2 } + 10 x = - 52x2+10x=−5

Solve the Equation by the Method of Your Choice $2 x ^ { 2 } + 10 x = - 5$