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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: $-3x^2-24x=49$

23.

Quadratic Equations

23.1

Characteristics of quadratic functions

23.2

Transformations of quadratic functions

23.3

Converting from general form to vertex form by completing the square

23.4

Solving quadratic equations by factoring

23.5

Solving quadratic equations by completing the square

23.6

Using quadratic formula to solve quadratic equations

23.7

Nature of roots of quadratic equations: the discriminant

23.8

System of linear equations

23.9

System of linear-quadratic equations

We have over 1180 practice questions in Algebra 1 for you to master.

Get Started Now23.1

Characteristics of quadratic functions

23.3

Converting from general form to vertex form by completing the square

23.4

Solving quadratic equations by factoring

23.5

Solving quadratic equations by completing the square

23.6

Using quadratic formula to solve quadratic equations

23.9

System of linear-quadratic equations