Completing the square

Definition

Completing the square is a method to solve quadratic equations by converting them into a perfect square trinomial. This facilitates easier solving and helps in deriving the quadratic formula.

5 Must Know Facts For Your Next Test

1. Completing the square involves adding and subtracting a specific value to create a perfect square trinomial.
2. The process often starts with moving the constant term to the other side of the equation.
3. The added value is derived from taking half of the coefficient of the linear term, squaring it, and adjusting both sides of the equation accordingly.
4. This method can be used to derive the quadratic formula: $ax^2 + bx + c = 0$.
5. It is particularly useful for solving quadratic equations when factoring is difficult or impossible.

Review Questions

• What is the purpose of completing the square in solving quadratic equations?
• How do you determine what value needs to be added and subtracted when completing the square?
• In which scenarios might completing the square be more advantageous than factoring?

Related terms

Quadratic Formula: A formula that provides solutions to a quadratic equation $ax^2 + bx + c = 0$ given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Perfect Square Trinomial: A quadratic expression that can be written as $(ax + b)^2$, resulting from $(ax)^2 + 2abx + b^2$.

Discriminant: The part of the quadratic formula under the square root symbol, $b^2 - 4ac$, which determines the nature and number of roots of a quadratic equation.