Solve the equation and write complex solutions in standard form. $$x ^ { 2 } - 6 x + 58 = 0$$
A) $x = 3 + 7 i , 3 - 7 i$
B) $x = 7 + 9 i , 7 - 9 i$
C) $x = 3 + 49 i , 3 - 49 i$
D) $x = 21 + 7 i , 21 - 7 i$
E) $x = 7 + 3 i , 7 - 3 i$

Question

Solve the equation and write complex solutions in standard form. $$x ^ { 2 } - 6 x + 58 = 0$$ 
A) $x = 3 + 7 i , 3 - 7 i$
B) $x = 7 + 9 i , 7 - 9 i$
C) $x = 3 + 49 i , 3 - 49 i$
D) $x = 21 + 7 i , 21 - 7 i$
E) $x = 7 + 3 i , 7 - 3 i$

Quizplus · Accepted Answer

Using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, with $a = 1$, $b = -6$, and $c = 58$, we find the discriminant $b^2 - 4ac = (-6)^2 - 4(1)(58) = 36 - 232 = -196$. The square root of $-196$ is $14i$, so the solutions are $x = \frac{6 \pm 14i}{2}$, which simplifies to $3 \pm 7i$.

Solve the Equation and Write Complex Solutions in Standard Form x2−6x+58=0x ^ { 2 } - 6 x + 58 = 0x2−6x+58=0

Solve the Equation and Write Complex Solutions in Standard Form $x ^ { 2 } - 6 x + 58 = 0$