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0. Fundamental Concepts of Algebra(0)

Algebraic Expressions
(0)

Exponents
(0)

Polynomials Intro
(0)

Multiplying Polynomials
(0)

Factoring Polynomials
(0)

Radical Expressions
(0)

Simplifying Radical Expressions
(0)

Rationalize Denominator
(0)

Rational Exponents
(0)

Pythagorean Theorem & Basics of Triangles
(0)

1. Equations and Inequalities(0)

Linear Equations
(0)

Rational Equations
(0)

The Imaginary Unit
(0)

Powers of i
(0)

Complex Numbers
(0)

Intro to Quadratic Equations
(0)

The Square Root Property
(0)

Completing the Square
(0)

The Quadratic Formula
(0)

Choosing a Method to Solve Quadratics
(0)

Linear Inequalities
(0)

2. Graphs(0)

Graphs and Coordinates
(0)

Two-Variable Equations
(0)

Lines
(0)

3. Functions & Graphs(0)

Intro to Functions & Their Graphs
(0)

Common Functions
(0)

Transformations
(0)

Function Operations
(0)

Function Composition
(0)

4. Polynomial Functions(0)

Quadratic Functions
(0)

Understanding Polynomial Functions
(0)

Graphing Polynomial Functions
(0)

5. Rational Functions(0)

Introduction to Rational Functions
(0)

Asymptotes
(0)

Graphing Rational Functions
(0)

6. Exponential and Logarithmic Functions(0)

Introduction to Exponential Functions
(0)

Graphing Exponential Functions
(0)

The Number e
(0)

Introduction to Logarithms
(0)

Graphing Logarithmic Functions
(0)

Properties of Logarithms
(0)

Solving Exponential and Logarithmic Equations
(0)

7. Measuring Angles(0)

Angles in Standard Position
(0)

Coterminal Angles
(0)

Complementary and Supplementary Angles
(0)

Radians
(0)

8. Trigonometric Functions on Right Triangles(0)

Trigonometric Functions on Right Triangles
(0)

Special Right Triangles
(0)

Cofunctions of Complementary Angles
(0)

Solving Right Triangles
(0)

9. Unit Circle(0)

Defining the Unit Circle
(0)

Trigonometric Functions on the Unit Circle
(0)

Common Values of Sine, Cosine, & Tangent
(0)

Reference Angles
(0)

Reciprocal Trigonometric Functions on the Unit Circle
(0)

10. Graphing Trigonometric Functions(0)

Graphs of the Sine and Cosine Functions
(0)

Phase Shifts
(0)

Graphs of Secant and Cosecant Functions
(0)

Graphs of Tangent and Cotangent Functions
(0)

11. Inverse Trigonometric Functions and Basic Trig Equations(0)

Inverse Sine, Cosine, & Tangent
(0)

Evaluate Composite Trig Functions
(0)

Linear Trigonometric Equations
(0)

12. Trigonometric Identities (0)

Introduction to Trigonometric Identities
(0)

Sum and Difference Identities
(0)

Double Angle Identities
(0)

Solving Trigonometric Equations Using Identities
(0)

13. Non-Right Triangles(0)

Law of Sines
(0)

Law of Cosines
(0)

Area of SAS & ASA Triangles
(0)

14. Vectors(0)

Geometric Vectors
(0)

Vectors in Component Form
(0)

Direction of a Vector
(0)

Unit Vectors and i & j Notation
(0)

Dot Product
(0)

Cross Product
(0)

15. Polar Equations(0)

Polar Coordinate System
(0)

Convert Points Between Polar and Rectangular Coordinates
(0)

Convert Equations Between Polar and Rectangular Forms
(0)

Graphing Other Common Polar Equations
(0)

16. Parametric Equations(0)

Graphing Parametric Equations
(0)

Eliminate the Parameter
(0)

Writing Parametric Equations
(0)

17. Graphing Complex Numbers(0)

Graphing Complex Numbers
(0)

Polar Form of Complex Numbers
(0)

Products and Quotients of Complex Numbers
(0)

Powers of Complex Numbers (DeMoivre's Theorem)
(0)

18. Systems of Equations and Matrices(0)

Two Variable Systems of Linear Equations
(0)

Introduction to Matrices
(0)

Determinants and Cramer's Rule
(0)

Graphing Systems of Inequalities
(0)

19. Conic Sections(0)

Introduction to Conic Sections
(0)

Circles
(0)

Ellipses: Standard Form
(0)

Parabolas
(0)

Hyperbolas at the Origin
(0)

Hyperbolas NOT at the Origin
(0)

20. Sequences, Series & Induction(0)

Sequences
(0)

Arithmetic Sequences
(0)

Geometric Sequences
(0)

21. Combinatorics and Probability(0)

Factorials
(0)

Combinatorics
(0)

Probability
(0)

22. Limits & Continuity(0)

Introduction to Limits
(0)

Finding Limits Algebraically
(0)

Continuity
(0)

23. Intro to Derivatives & Area Under the Curve(0)

Tangent Lines & Derivatives
(0)

Limits at Infinity
(0)

Limits of Sequences
(0)

Area Under a Curve
(0)

1. Equations and Inequalities

Completing the Square

1. Equations and Inequalities

Completing the Square: Videos & Practice Problems

Video Lessons Practice Worksheet

20 problems

Problem 1Multiple Choice

Consider the following equations and solve for all values of x that will satisfy them. z₁ = x, z₂ = -6/x and z₁ + z₂ = -1

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Problem 2Multiple Choice

Perform completing the square to solve the following equation: 3x² - 8x + 4 = 0

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Problem 3Multiple Choice

By using the quadratic formula, solve the following equation.

x² - 16x + 73 = 0

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Problem 4Multiple Choice

For the following equation, complete the square:

x² - (8/7)x

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Problem 5Multiple Choice

Use any method to solve the given equation. 9x² -30x +50 = 0

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Problem 6Multiple Choice

By applying the square root property, solve:

11(g + 5)² = 121

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Problem 7Multiple Choice

What is the primary purpose of completing the square in solving quadratic equations?

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Problem 8Multiple Choice

In which scenario is completing the square most appropriate?

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Problem 9Multiple Choice

Simplify the equation 2x^2 + 8x + 5 = 0 to the form x^2 + bx = c.

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Problem 10Multiple Choice

For the equation x^2 + 10x = 3, what value should be added to both sides to complete the square?

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Problem 11Multiple Choice

After adding 16 to both sides of the equation x^2 + 8x = 0, factor the resulting expression.

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Problem 12Multiple Choice

Solve the equation (x + 5)^2 = 9 using the square root property.

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Problem 13Multiple Choice

Express the solution of the equation (x + 3)^2 = 7 in the form of negative b over 2 plus or minus the square root of the constant.

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Problem 14Multiple Choice

Why does adding (b/2)^2 to both sides of the equation x^2 + bx = c create a perfect square trinomial?

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Problem 15Multiple Choice

Complete the square for the equation x^2 + 12x + 20 = 0 and find the solutions.

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Problem 16Multiple Choice

Which of the following statements best evaluates the effectiveness of completing the square as a method for solving quadratic equations?

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Problem 17Multiple Choice

Which of the following is a key step in completing the square?

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Problem 18Multiple Choice

Why is completing the square a good choice when the coefficient of x is even?

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Problem 19Multiple Choice

Transform the equation 3x^2 + 12x - 9 = 0 to the form x^2 + bx = c.

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Problem 20Multiple Choice

For the equation x^2 + 14x = 5, what value should be added to both sides to complete the square?

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The Square Root Property Practice Problems The Quadratic Formula Practice Problems

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Completing the Square: Videos & Practice Problems

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Conic Sections Calculator

Equation Solver

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FOIL Calculator (Binomial Multiplication)

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