Question
$$x^2+2(x+2)x+x^2+3 = 0$$
Answer
$$ \begin{matrix}x_1 = -\dfrac{ 1 }{ 2 }+\dfrac{\sqrt{ 2 }}{ 2 }i & x_2 = -\dfrac{ 1 }{ 2 }-\dfrac{\sqrt{ 2 }}{ 2 }i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^2+2(x+2)x+x^2+3 &= 0&& \text{simplify left side} \\[1 em]x^2+(2x+4)x+x^2+3 &= 0&& \\[1 em]x^2+2x^2+4x+x^2+3 &= 0&& \\[1 em]3x^2+4x+x^2+3 &= 0&& \\[1 em]4x^2+4x+3 &= 0&& \\[1 em] \end{aligned} $$
$ 4x^{2}+4x+3 = 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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