Solving Quadratic Equations

To solve the given equation by factoring, we will have to factor a perfect square trinomial.

a^{2} \pm 2 a b + b^{2} \Leftrightarrow (a \pm b)^{2}

Before we begin, let's rewrite the equation with all the non-zero terms on the left-hand side.

0 = x^{2} + 6 x + 9 \Leftrightarrow x^{2} + 6 x + 9 = 0

We see that there is no GCF to factor out. Let's factor the left-hand side and then solve the equation.

x^{2} + 6 x + 9 = 0

a^{2} + 2 a b + b^{2} = (a + b)^{2}

(x + 3)^{2} = 0

LHS = RHS

x + 3 = \pm 0

CalcRootCalculate root

x + 3 = \pm 0

LHS - 3 = RHS - 3

x = - 3

The only solution to this equation is

x = - 3 .

Solving Quadratic Equations 1.7 - Solution