Use the quadratic formula to find the exact solutions.
-$$x ^ { 2 } + 35 = 5 x$$
A) $\frac { 5 } { 2 } \pm \frac { \sqrt { 115 } } { 2 } \mathrm { i }$
B) 0,5
C) $- 5,5$
D) $\frac { 5 } { 2 } \pm \frac { 5 } { 2 } \mathrm { i }$

Question

Quizplus · Accepted Answer

First, rewrite the equation in standard form: $x^2 - 5x + 35 = 0$. Using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$, with $a = 1$, $b = -5$, and $c = 35$, we find $x = \frac{5 \pm \sqrt{(-5)^2-4(1)(35)}}{2(1)} = \frac{5 \pm \sqrt{25-140}}{2} = \frac{5 \pm \sqrt{-115}}{2}$. This simplifies to $\frac{5}{2} \pm \frac{\sqrt{115}}{2}i$, matching choice A.

Use the Quadratic Formula to Find the Exact Solutions x2+35=5xx ^ { 2 } + 35 = 5 xx2+35=5x

Use the Quadratic Formula to Find the Exact Solutions $x ^ { 2 } + 35 = 5 x$