Question

x^2+10x=-89

Answer 1

easiest to complete the square for this one
you are going to get two complex zeros

Answer 2

start with
\[(x+5)^2=-89+25\] and go from there

Answer 3

\[x^2+10x+25=-64?\]

Answer 4

\[x^2+10x = -89\]
completing the square\[x^2+10x+25 = -89+25\]\[(x+5)^2=-64\]
now take the square root\[x+5 = \sqrt{-64}\]
solve this for \(x\), using \(i=\sqrt{-1}\)

Answer 5

so then -5+8i?

Answer 6

great work, now you can test this solution, in the original equation
\[x^2+10x=-89\]

If \(x=-5+8i\) is the solution
then following equation should be true
\[(-5+8i)^2+10(-5+8i)=-89\]