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Solving Quadratic Equations

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Questions and Answers

What is the first step taken to rewrite the equation?

Adding 6 to both sides

Subtracting 6 from both sides

Rearranging the entire equation

Subtracting 3x from both sides (correct)

What does the quadratic equation simplify to after combining like terms?

x² - x - 2 = 0 (correct)

x² + x + 2 = 0

x² + 5x - 8 = 0

2x² + 2x - 6 = 0

What is the nature of the equation presented?

It is a quadratic equation (correct)

It is a linear equation

It is a cubic equation

It is a polynomial of degree 4

Which operation is applied to both sides of the equation to isolate the quadratic form?

<p>Subtraction of a variable</p> Signup and view all the answers

What is the standard form of a quadratic equation?

<p>ax² + bx + c = 0</p> Signup and view all the answers

Study Notes

Solving Quadratic Equations

The equation x² + 2x - 8 = 3x - 6 represents a quadratic equation because it has a term with x².
The first step in solving the equation is to bring all terms to one side by subtracting 3x and adding 6 to both sides.
This results in the simplified equation x² - x - 2 = 0.
The simplified equation has the form ax² + bx + c = 0, which is standard form for quadratic equations.
To solve this equation, we can use the quadratic formula or factoring techniques.

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Description

This quiz focuses on solving quadratic equations, specifically through the example x² + 2x - 8 = 3x - 6. Participants will learn how to simplify the equation and solve it using methods like the quadratic formula or factoring. It's an essential skill in algebra that builds a strong foundation for more advanced mathematics.