Find the real solutions, if any, of the equation. Use the quadratic formula.
-$$x ^ { 2 } + 7 x + 5 = 0$$
A) $\left\{ \frac { - 7 - \sqrt { 29 } } { 2 } , \frac { - 7 + \sqrt { 29 } } { 2 } \right\}$
B) $\left\{ \frac { - 7 - \sqrt { 29 } } { 14 } , \frac { - 7 + \sqrt { 29 } } { 14 } \right\}$
C) $\left\{ \frac { - 7 - \sqrt { 69 } } { 2 } , \frac { - 7 + \sqrt { 69 } } { 2 } \right\}$
D) $\left\{ \frac { 7 - \sqrt { 29 } } { 2 } , \frac { 7 + \sqrt { 29 } } { 2 } \right\}$

Question

Quizplus · Accepted Answer

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. For the equation $x^2 + 7x + 5 = 0$, $a = 1$, $b = 7$, and $c = 5$. Plugging these into the formula gives $x = \frac{-7 \pm \sqrt{49 - 20}}{2}$, which simplifies to $x = \frac{-7 \pm \sqrt{29}}{2}$, matching choice A.

Find the Real Solutions, If Any, of the Equation x2+7x+5=0x ^ { 2 } + 7 x + 5 = 0x2+7x+5=0

Find the Real Solutions, If Any, of the Equation $x ^ { 2 } + 7 x + 5 = 0$