# How do you solve using the completing the square method x^2 + 2x = 0?

Mar 22, 2016

Please follow the process given below. Answer is $x = 0$ and $x = - 2$

#### Explanation:

We know that ${\left(x + a\right)}^{2} = {x}^{2} + 2 a x + {a}^{2}$, hence to complete say ${x}^{2} + b x$ to a square we should add and subtract, square of half the coefficient of $x$ i.e. ${\left(\frac{b}{2}\right)}^{2}$.

As the equation is ${x}^{2} + 2 x = 0$, we have to add and subtract ${\left(\frac{2}{2}\right)}^{2} = 1$ and equation becomes

${x}^{2} + 2 x + 1 - 1 = 0$ and now this can be written as

${\left(x + 1\right)}^{2} - 1 = 0$ or

$\left(\left(x + 1\right) + 1\right) \times \left(\left(x + 1\right) - 1\right) = 0$ or

((x+2)xx x=0 i.e. either $x = 0$ or $x + 2 = 0$ or $x = - 2$