Solve by Factoring x^2+2ax+a^2=0

$x^{2} + 2 a x + a^{2} = 0$

Step 1

Factor using the perfect square rule.

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$2 a x = 2 \cdot x \cdot a$

Rewrite the polynomial.

$x^{2} + 2 \cdot x \cdot a + a^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = a$ .

${(x + a)}^{2} = 0$

Step 2

Set the $x + a$ equal to $0$ .

$x + a = 0$

Step 3

Subtract $a$ from both sides of the equation.

$x = - a$