Question

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

x = or x =

Answer 1

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

Answer 2

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

Step-by-step 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 √(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=(-10\pm √((-10)^2-4(1)(41)))/(2(1))`

We evaluate to obtain;

`x=(-10\pm √(100-164))/(2(1))`

`x=(-10\pm √(-64))/(2)`

`x=(-10\pm √(64)√(-1))/(2)`

Note that in complex numbers;

`i=√(-1)`

This implies that;

`x=(-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`