Question

Solve for x over the complex numbers. x 2 +4x+13=0 Enter your answers in the boxes in standard form.

Answer 1

The solutions are x=-2+3i and x=-2-3i

Explanation:

we know that

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`x^(2) +4x+13=0`

so

`a=1\\b=4\\c=13`

substitute in the formula

`x=\frac{-4(+/-)\sqrt{4^(2)-4(1)(13)}} {2(1)}`

`x=\frac{-4(+/-)√(-36)} {2}`

Remember that

`i^(2) =-1\\i=√(-1)`

substitute

`x=\frac{-4(+/-)6i} {2}`

`x_1=\frac{-4(+)6i} {2}=-2+3i`

`x_2=\frac{-4(-)6i} {2}=-2-3i`

therefore

The solutions are x=-2+3i and x=-2-3i