6 Determine the Most Efficient Method to Use When Solving a Quadratic Equation
-$$( x + 10 ) ( x - 7 ) = 5$$
A) $\left\{ \frac { - 3 \pm \sqrt { 309 } } { 2 } \right\}$
B) $\left\{ \frac { 3 \pm \sqrt { 309 } } { 2 } \right\}$
C) $\left\{ \frac { - 3 \pm i \sqrt { 309 } } { 2 } \right\}$
D) $\left\{ \frac { 3 \pm \mathrm { i } \sqrt { 309 } } { 2 } \right\}$

Question

Quizplus · Accepted Answer

First, expand the given equation to get $x^2 + 3x - 70 = 5$, then simplify to $x^2 + 3x - 75 = 0$. Using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, with $a = 1$, $b = 3$, and $c = -75$, results in $x = \frac{-3 \pm \sqrt{9 + 300}}{2}$, which simplifies to $\frac{-3 \pm \sqrt{309}}{2}$.

6 Determine the Most Efficient Method to Use When Solving (x+10)(x−7)=5( x + 10 ) ( x - 7 ) = 5(x+10)(x−7)=5

6 Determine the Most Efficient Method to Use When Solving $( x + 10 ) ( x - 7 ) = 5$