Solve the equation using the quadratic formula.
-$$x ^ { 2 } - 3 = \sqrt { 7 } x$$
A) $x = \frac { \sqrt { 7 } - \sqrt { 19 } } { 2 }$ or $x = \frac { \sqrt { 7 } + \sqrt { 19 } } { 2 }$
B) $x = - \frac { 1 } { \sqrt { 7 } }$ or $x = \frac { 1 } { \sqrt { 7 } }$
C) $x = - \sqrt { 7 }$ or $x = \sqrt { 7 }$
D) $x = 1$ or $x = - 1$

Question

Quizplus · Accepted Answer

First, rearrange the equation to standard form: $x^2 - \sqrt{7}x - 3 = 0$. Then, apply the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with $a = 1$, $b = -\sqrt{7}$, and $c = -3$. This yields $x = \frac{\sqrt{7} \pm \sqrt{(\sqrt{7})^2 - 4(1)(-3)}}{2(1)} = \frac{\sqrt{7} \pm \sqrt{7 + 12}}{2} = \frac{\sqrt{7} \pm \sqrt{19}}{2}$.

Solve the Equation Using the Quadratic Formula x2−3=7xx ^ { 2 } - 3 = \sqrt { 7 } xx2−3=7​x

Solve the Equation Using the Quadratic Formula $x ^ { 2 } - 3 = \sqrt { 7 } x$