# 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 $X^2$
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
• Introduction
Solve by completing the square: $2{x^2} - 12x + 10 = 0$

• 1.
Solving a quadratic equation with TWO REAL SOLUTIONS
Solve by completing the square: $x^2+10x+6=0$

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

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