Question

Solve for x over the complex numbers. x^2+8x+20=0

X= or X=

Answer 1

Answer:you can use the quadratic formula but if you have to factor do the following:

x^2+8x+20=0

add -4 to both sides of the equation to complete the square

x^2+8x+20+(-4)=0+(-4)

x^2+8x+16=-4

(x+4)^2=-4

take the square root of both sides

x+4=+sqrt(-4)

x+4=+sqrt[(4)(-1)]

x+4=+2sqrt(-1) where sqrt(-1)=i, a complex number

x+4=+2i

x=-4+2i

x=-4+2i and x=-4-2i

you would get the same answer using the quadratic formula

Explanation:

Answer 2

Steps:

`x=(-8+√(8^2-4\cdot \:1\cdot \:20))/(2\cdot \:1): -4+2i`

`x=(-8-√(8^2-4\cdot \:1\cdot \:20))/(2\cdot \:1) -4-2i`

=\frac{-8-\sqrt{16}i}{2\cdot \:1}
`=-8-√(16)i`

`=(-8-√(16)i)/(2)`

`=(-8-4i)/(2)`

`=-2\left(2+i\right)`

`=-4-2i`

`x=-4+2i,\:x=-4-2i`