Question
$$2(c+5)+2c^2 = 0$$
Answer
$$ \begin{matrix}c_1 = -\dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 19 }}{ 2 }i & c_2 = -\dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 19 }}{ 2 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2(c+5)+2c^2 &= 0&& \text{simplify left side} \\[1 em]2c+10+2c^2 &= 0&& \\[1 em]2c^2+2c+10 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}+2x+10 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
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