Question

Solve: x^2 - 7x = -13

Answer 1

$x^2-7x=-13$

Rewrite the equation as:

$x^2-7x+13=0$

use the quadratic formula:

$\begin{gathered} ax^2+bx+c=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \end{gathered}$

so:

$\begin{gathered} x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4(1)(13)}}{2(1)} \\ x=\frac{-7\pm\sqrt[]{49-52}}{2} \\ x=\frac{-7\pm\sqrt[]{-3}}{2} \\ x=\frac{1}{2}(7\pm\sqrt[]{3}i) \end{gathered}$