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- Quadratic Equations and Inequalities

Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

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Get Started Now- Intro Lesson11:49
- Lesson: 14:35
- Lesson: 28:10
- Lesson: 39:03

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

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

10.

Quadratic Equations and Inequalities

10.1

Solving quadratic equations by factoring

10.2

Solving quadratic equations by completing the square

10.3

Using quadratic formula to solve quadratic equations

10.4

Nature of roots of quadratic equations: The discriminant

10.5

Applications of quadratic equations

10.6

Solving quadratic inequalities

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