Solving quadratic equations by completing the square
Topic Notes
When a quadratic equation cannot be factorized, we can use the method of completing the square to solve the equation.
4-step approach:
1. isolate X's on one side of the equation
2. factor out the leading coefficient of
3. "completing the square"
• X-side: inside the bracket, add (half of the coefficient of
• Y-side: add [ leading coefficient (half of the coefficient of ]
4. clean up
• X-side: convert to perfect-square form
• Y-side: clean up the algebra
1. isolate X's on one side of the equation
2. factor out the leading coefficient of
3. "completing the square"
• X-side: inside the bracket, add (half of the coefficient of
• Y-side: add [ leading coefficient (half of the coefficient of ]
4. clean up
• X-side: convert to perfect-square form
• Y-side: clean up the algebra
Basic Concepts
- Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2
- Completing the square
- Converting from general to vertex form by completing the square
- Shortcut: Vertex formula