Solving quadratic equations by completing the square

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.

Lessons

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
  • 1.
    Solve by completing the square: 2x212x+10=02{x^2} - 12x + 10 = 0

  • 2.
    Solving a quadratic equation with TWO REAL SOLUTIONS
    Solve by completing the square: x2+10x+6=0x^2+10x+6=0

  • 3.
    Solving a quadratic equation with ONE (REPEATED) REAL SOLUTION
    Solve by completing the square: 9x2+25=30x9x^2+25=30x

  • 4.
    Solving a quadratic equation with TWO COMPLEX SOLUTIONS
    Solve by completing the square: 3x224x=49-3x^2-24x=49