Solve the quadratic equation and express all nonreal complex solutions in terms of i.
-$$\mathrm { x } ^ { 2 } + 35 = 5 \mathrm { x }$$
A) $\{ 0,5 \}$
B) $\left\{ \frac { 5 } { 2 } \pm \frac { 5 } { 2 } i \right\}$
C) $\{ - 5,5 \}$
D) $\left\{ \frac { 5 } { 2 } \pm \frac { \sqrt { 115 } } { 2 } \mathrm { i } \right\}$

Question

Quizplus · Accepted Answer

The equation can be rewritten as $x^2 - 5x + 35 = 0$. Using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 1$, $b = -5$, and $c = 35$, we find the discriminant $b^2 - 4ac = 25 - 140 = -115$. The solutions are $\frac{5 \pm \sqrt{-115}}{2}$, which simplifies to $\frac{5}{2} \pm \frac{\sqrt{115}}{2}i$.

Solve the Quadratic Equation and Express All Nonreal Complex Solutions x2+35=5x\mathrm { x } ^ { 2 } + 35 = 5 \mathrm { x }x2+35=5x

Solve the Quadratic Equation and Express All Nonreal Complex Solutions $\mathrm { x } ^ { 2 } + 35 = 5 \mathrm { x }$