Answer
$x_{1}=\sqrt{11}i$ and $x_{2}=\sqrt{11}i$
Work Step by Step
Given $5x^2+55=0$
$1.)$ Divide by 5 both sides of the equation: $5x^2+55=0 \longrightarrow x^2+11=0$
$2.)$ Use the quadratic formula: $\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$
$a=1, \ b=0, \ c = 11$
$\dfrac{-0\pm \sqrt{0^2-4\times 1 \times 11}}{2\times 1} = \dfrac{\pm \sqrt{-44}}{2} = \dfrac{\pm \sqrt{4\times (-11)}}{2} = \dfrac{\pm 2\sqrt{-11}}{2} = \pm \sqrt{-11} = \pm \sqrt{11}i$
Therefore the solutions are $x_{1}=\sqrt{11}i$ and $x_{2}=\sqrt{11}i$
