Choosing a Method

Choose the method from the form of the equation. Factoring works well when you can find the factor pair easily. Taking square roots works when the equation is a square equal to a number. The quadratic formula works for every quadratic equation, and the discriminant tells you whether the solutions are real.

For $x^{2} = 64$, take square roots to get $x = \pm 8$. For $x^{2}+5x+4 = 0$, the pair 1 and 4 gives $\left(x+1\right)\left(x+4\right) = 0$. For $x^{2}+3x+1 = 0$, no pair of whole numbers works, so use the quadratic formula.

The discriminant can help you choose. When the coefficients are whole numbers, a discriminant that is a perfect square means the solutions are whole numbers or fractions, so factoring may work. A positive discriminant that is not a perfect square means the solutions have a square root sign, so use the quadratic formula or complete the square. A negative discriminant means there are no real solutions.