solve for x in the equation $x^{2}-12x + 59 = 0$.\n$x=-12pmsqrt{85}$\n$x=-6pmsqrt{23}i$\n$x=6pmsqrt{23}i$\n$x…

Explanation:

Step1: Identify coefficients

For the quadratic equation $ax^{2}+bx + c = 0$, here $a = 1$, $b=-12$, $c = 59$.

Step2: Use quadratic - formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute the values: $x=\frac{-(-12)\pm\sqrt{(-12)^{2}-4\times1\times59}}{2\times1}$.

Step3: Calculate discriminant

First, calculate $b^{2}-4ac=(-12)^{2}-4\times1\times59 = 144 - 236=-92$.

Step4: Simplify the expression

$x=\frac{12\pm\sqrt{-92}}{2}=\frac{12\pm\sqrt{4\times23\times(-1)}}{2}=\frac{12\pm2\sqrt{23}i}{2}=6\pm\sqrt{23}i$.

Answer:

$x = 6\pm\sqrt{23}i$