Page 2: Solving Quadratic Equations of the Form x² = a

This page delves into the specific case of solving quadratic equations in the form x² = a, providing clear examples and solution methods.

Definition: For an equation in the form x² = a, there are always two solutions because both (√a)² and $-√a$² equal a.

Example: Two detailed examples are provided:

1. Solving x² = 5: Solutions are x = √5 and x = -√5
2. Solving x² = 100: Solutions are x = 10 and x = -10

Highlight: The general solution format for x² = a is: x = √a or x = -√a, where a is a positive number

Page 1: Fundamental Equation Solving Principles

This page introduces the core concepts of equation solving and presents key mathematical properties. The content focuses on systematic approaches to solving different types of equations, from linear to more complex forms.

Definition: Solving an equation means determining the values of the unknown variable for which the equality holds true. These values are called solutions to the equation.

Example: For a linear equation 3x + 7 = 13, the solution process involves:

1. Subtracting 7 from both sides: 3x = 6
2. Dividing both sides by 3: x = 2

Highlight: Key mathematical operations and their corresponding inverse operations:

• For multiplication, divide both sides
• For division, multiply both sides
• For subtraction, add to both sides
• For addition, subtract from both sides

Vocabulary: Properties of equations:

• Property 1: If axb = 0, then a = 0 or b = 0
• Property 2: A product equals zero if at least one of its factors equals zero