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- Solving Quadratic Equations
Solving quadratic equations by completing the square
- Intro Lesson11:49
- Lesson: 14:35
- Lesson: 28:10
- Lesson: 39:03
Solving quadratic equations by completing the square
When a quadratic equation cannot be factorized, we can use the method of completing the square to solve the equation.
Basic Concepts: Factoring perfect square trinomials: (a+b)2=a2+2ab+b2 or (a−b)2=a2−2ab+b2, Completing the square, Converting from general to vertex form by completing the square, Shortcut: Vertex formula
Related Concepts: System of linear-quadratic equations, System of quadratic-quadratic equations, Graphing quadratic inequalities in two variables, Graphing systems of quadratic inequalities
Lessons
4-step approach:
1. isolate X's on one side of the equation
2. factor out the leading coefficient of X2
3. "completing the square"
• X-side: inside the bracket, add (half of the coefficient of X)2
• Y-side: add [ leading coefficient ⋅ (half of the coefficient of X)2 ]
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 X2
3. "completing the square"
• X-side: inside the bracket, add (half of the coefficient of X)2
• Y-side: add [ leading coefficient ⋅ (half of the coefficient of X)2 ]
4. clean up
• X-side: convert to perfect-square form
• Y-side: clean up the algebra
- IntroductionSolve by completing the square: 2x2−12x+10=0
- 1.Solving a quadratic equation with TWO REAL SOLUTIONS
Solve by completing the square: x2+10x+6=0 - 2.Solving a quadratic equation with ONE (REPEATED) REAL SOLUTION
Solve by completing the square: 9x2+25=30x - 3.Solving a quadratic equation with TWO COMPLEX SOLUTIONS
Solve by completing the square: −3x2−24x=49