Completing the square

Definition

Completing the square is a method used to solve quadratic equations by transforming them into a perfect square trinomial. This technique allows for easier identification of the roots of the equation.

5 Must Know Facts For Your Next Test

1. To complete the square, you first need to ensure that the coefficient of $x^2$ is 1. If not, divide the entire equation by that coefficient.
2. Move the constant term to the other side of the equation before completing the square.
3. The next step involves adding and subtracting $(\frac{b}{2})^2$ within the equation, where $b$ is the coefficient of $x$.
4. After completing these steps, you can rewrite one side of the equation as a binomial squared: $(x + \frac{b}{2})^2$.
5. Finally, solve for $x$ by taking the square root of both sides and then isolating $x$.

Review Questions

• What is the first step in completing the square when solving a quadratic equation?
• How do you determine what value to add and subtract when completing the square?
• Once you have rewritten one side of an equation as a binomial squared, what are your next steps?

Related terms

Quadratic Equation: An equation in which the highest power of an unknown variable is a square; typically in standard form as $ax^2 + bx + c = 0$.

Perfect Square Trinomial: A trinomial that can be factored into a binomial squared; it has the form $(a+b)^2 = a^2 + 2ab + b^2$.

Discriminant: $b^2 - 4ac$, part of the quadratic formula that determines whether roots are real or complex.