Solving quadratic equations by completing the square

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Intros
Lessons
  1. Solve by completing the square: 2x2−12x+10=02{x^2} - 12x + 10 = 0
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Examples
Lessons
  1. Solving a quadratic equation with TWO REAL SOLUTIONS
    Solve by completing the square: x2+10x+6=0x^2+10x+6=0
    1. Solving a quadratic equation with ONE (REPEATED) REAL SOLUTION
      Solve by completing the square: 9x2+25=30x9x^2+25=30x
      1. Solving a quadratic equation with TWO COMPLEX SOLUTIONS
        Solve by completing the square: −3x2−24x=49-3x^2-24x=49
        Topic Notes
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        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 X2X^2
        3. "completing the square"
        • X-side: inside the bracket, add (half of the coefficient of X)2X)^2
        • Y-side: add [ leading coefficient ⋅\cdot (half of the coefficient of X)2X)^2 ]
        4. clean up
        • X-side: convert to perfect-square form
        • Y-side: clean up the algebra
        Basic Concepts
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        Related Concepts
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