Solve by using the quadratic formula: $$z ^ { 2 } - 2 z = 51$$
A) $1 - 2 \sqrt { 13 } , 1 + 2 \sqrt { 13 }$
B) $- 1 - 14 \sqrt { 13 } , - 1 + 14 \sqrt { 13 }$
C) $- 2 \sqrt { 13 } , 2 \sqrt { 13 }$
D) $1 - 14 \sqrt { 13 } , - 1 + 3 \sqrt { 13 }$
E) $- 1 + 2 \sqrt { 13 } , - 1 - 2 \sqrt { 13 }$

Question

Quizplus · Accepted Answer

First, rewrite the equation in standard form: $z^2 - 2z - 51 = 0$. Using the quadratic formula, $z = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, with $a = 1$, $b = -2$, and $c = -51$, we find $z = \frac{2 \pm \sqrt{4 + 204}}{2} = \frac{2 \pm \sqrt{208}}{2} = 1 \pm 2\sqrt{13}$.

Solve by Using the Quadratic Formula z2−2z=51z ^ { 2 } - 2 z = 51z2−2z=51

Solve by Using the Quadratic Formula $z ^ { 2 } - 2 z = 51$