Question

Solve for x over the complex numbers. x2+10x+41=0 Enter your answers in the boxes.
x = or x =

Answer 1

ANSWER: $x=-5-4i$ or $x=-5+4i$

Explanation:

The equation given to us is

$x^2+10x+41=0$.

One way to solve this equation is to use the quadratic formula;

$x=\frac{-b\pm \sqrt{b^2-4ac}} {2a}$

When we compare $x^2+10x+41=0$ to the general quadratic equation $ax^2+bx+c=0$.

$a=1,b=10,c=41$

When we substitute these values in to the formula, we obtain;

$x=\frac{-10\pm \sqrt{(-10)^2-4(1)(41)}}{2(1)}$

We evaluate to obtain;

$x=\frac{-10\pm \sqrt{100-164}}{2(1)}$

$x=\frac{-10\pm \sqrt{-64}}{2}$

$x=\frac{-10\pm \sqrt{64}\sqrt{-1}}{2}$

Note that in complex numbers;

$i=\sqrt{-1}$

This implies that;

$x=\frac{-10\pm 8i}{2}$

$x=-5\pm 4i$

When we split the plus or minus sign we get;

$x=-5-4i$

or

$x=-5+4i$

Answer 2

Answer:

x=-5-4i or x= -5+4i