Solving a quadratic equation with TWO REAL SOLUTIONS
Solve by completing the square: x2+10x+6=0
Solving a quadratic equation with ONE (REPEATED) REAL SOLUTION
Solve by completing the square: 9x2+25=30x
Solving a quadratic equation with TWO COMPLEX SOLUTIONS
Solve by completing the square: −3x2−24x=49
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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 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
