# Solving quadratic equations by completing the square

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