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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
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18.
Quadratic functions
18.1
Characteristics of quadratic functions
18.2
Graphing parabolas for given quadratic functions
18.3
Finding the quadratic functions for given parabolas
18.4
Solving quadratic equations by factoring
18.5
Solving quadratic equations by completing the square
18.6
Using quadratic formula to solve quadratic equations
18.7
Nature of roots of quadratic equations: the discriminant