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 = ±8. For x^2 + 5x + 4 = 0, the pair 1 and 4 gives (x + 1)(x + 4) = 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.