Use the quadratic formula to find the exact solutions.
-$$x ^ { 2 } = 15 + 3 x$$
A) 3,15
B) $\frac { 3 \pm \sqrt { 69 } } { 2 }$
C) $3 \pm \sqrt { 69 } \mathrm { i }$
D) $\frac { 3 } { 2 } \pm \frac { \sqrt { 69 } } { 2 } \mathrm { i }$

Question

Quizplus · Accepted Answer

First, rearrange the equation to standard form: $x^2 - 3x - 15 = 0$. Then, apply the quadratic formula $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ with $a = 1$, $b = -3$, and $c = -15$. This gives $x = \frac{3 \pm \sqrt{(-3)^2-4(1)(-15)}}{2(1)} = \frac{3 \pm \sqrt{69}}{2}$.

Use the Quadratic Formula to Find the Exact Solutions x2=15+3xx ^ { 2 } = 15 + 3 xx2=15+3x

Use the Quadratic Formula to Find the Exact Solutions $x ^ { 2 } = 15 + 3 x$