Answer
$x^2+100=0$.
Work Step by Step
The solutions are:
$\Rightarrow x=-10i$ or $x=10i$
Obtain zero on one side of each equations.
$\Rightarrow x+10i=0$ or $x-10i=0$
Apply zero-product principle in reverse.
$\Rightarrow (x+10i)(x-10i)=0$
Multiply conjugates using $(a+b)(a-b)=a^2-b^2$
$\Rightarrow x^2-(10i)^2=0$
Simplify.
$\Rightarrow x^2-100i^2=0$
Use $i^2=-1$.
$\Rightarrow x^2-100(-1)=0$
Simplify.
$\Rightarrow x^2+100=0$
Hence, the quadratic equation is $x^2+100=0$.
