Solving Quadratic Equations By Completing the Square Summary

Key Concepts

• Binomial Squares Pattern If \(a,b\) are real numbers,
  \({\left(a+b\right)}^{2}={a}^{2}+2ab+{b}^{2}\)
  
  \({\left(a-b\right)}^{2}={a}^{2}-2ab+{b}^{2}\)
  
• Complete a Square
  To complete the square of \({x}^{2}+bx\):
  1. Identify \(b\), the coefficient of \(x\).
  2. Find \({\left(\frac{1}{2}b\right)}^{2}\), the number to complete the square.
  3. Add the \({\left(\frac{1}{2}b\right)}^{2}\) to \({x}^{2}+bx\).

Glossary

completing the square

Completing the square is a method used to solve quadratic equations.