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Get Started Now- Lesson: 111:49
- Lesson: 24:35
- Lesson: 38:10
- Lesson: 49:03

When a quadratic equation cannot be factorized, we can use the method of completing the square to solve the equation.

Basic concepts: Factoring perfect square trinomials: $(a + b)^2 = a^2 + 2ab + b^2$ or $(a - b)^2 = a^2 - 2ab + b^2$, Completing the square, Converting from general to vertex form by completing the square, Shortcut: Vertex formula,

Related concepts: System of linear-quadratic equations, System of quadratic-quadratic equations, Graphing quadratic inequalities in two variables, Graphing systems of quadratic inequalities,

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

1. isolate X’s on one side of the equation

2. factor out the

3. “completing the square”

• X-side: inside the bracket, add (half of the coefficient of $X)^2$

• Y-side: add [

4. clean up

• X-side: convert to perfect-square form

• Y-side: clean up the algebra

- 1.Solve by completing the square: $2{x^2} - 12x + 10 = 0$
- 2.
**Solving a quadratic equation with TWO REAL SOLUTIONS**

Solve by completing the square: $x^2+10x+6=0$ - 3.
**Solving a quadratic equation with ONE (REPEATED) REAL SOLUTION**

Solve by completing the square: $9x^2+25=30x$ - 4.
**Solving a quadratic equation with TWO COMPLEX SOLUTIONS**

Solve by completing the square: $-3x^2-24x=49$

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