solve for x in the equation $x^{2}-8x + 41=0$.\n$x=-4pmsqrt{37}i$\n$x=-4pm5i$\n$x = 4pmsqrt{37}i$\n$x=4pm5i$

Explanation:

Step1: Identify coefficients

For the quadratic equation $ax^{2}+bx + c = 0$, here $a = 1$, $b=-8$, $c = 41$.

Step2: Use quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Substitute the values: $x=\frac{-(-8)\pm\sqrt{(-8)^{2}-4\times1\times41}}{2\times1}=\frac{8\pm\sqrt{64 - 164}}{2}=\frac{8\pm\sqrt{- 100}}{2}$.

Step3: Simplify the square - root and the fraction

Since $\sqrt{-100}=\sqrt{100}\times\sqrt{-1}=10i$, then $x=\frac{8\pm10i}{2}=4\pm5i$.

Answer:

$x = 4\pm5i$