How to Solve Quadratic Equations Using the Formula Method

What Is a Quadratic Equation?

A quadratic equation is any equation that can be written in the form:

ax²+bx+c=0

Where:

• a, b, and c are constants
• x is the variable
• a ≠ 0

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Examples of quadratic equations:

• 2x²+3x−5=0
• x²−4x+4=0
• 5x²−20=0

The Quadratic Formula

To solve any quadratic equation, you can use the quadratic formula:

Where:

• a, b, and c are the coefficients from the quadratic equation
• The symbol ± means there are usually two solutions

Step-by-Step Guide

Let’s begin through an example together.

Example: Solve

2x²+3x−5=0

Step 1: Identify a, b, and c

a=2, b=3, c=−5

Step 2: Plug into the formula

Step 3: Now, let’s solve both possibilities

Final Answer: x = 1 or x = -2.5

Tips for Successful Quadratic Equations is:

Remember the Order: a, b, c

Always write the equation in standard form before extracting values.

Check the Discriminant

That’s the part under the square root:

This tells you how many solutions you’ll have:

• If it’s positive: 2 real solutions
• If it’s zero: 1 real solution
• If it’s negative: No real solution (you’ll get complex numbers)

Common Mistakes to Avoid When Solving Quadratic Especially the Use of Formula are:

• Plugging the wrong signs for a, b, or c
• Forgetting to square b (i.e., b²)
• Not simplifying the square root correctly
• Dividing only part of the numerator by 2a

Practice Questions

1. Solve:

x²−6x+9=0

2. Solve:

3x²+x−2=0

3. Solve:

5x²−10x+5=0

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Real-World Applications

For your information, Quadratic equations are used in:

• Physics (projectile motion)
• Business (profit and revenue curves)
• Engineering
• Architecture
• Even in calculating areas and dimensions!

Summary

The Quadratic Formula is a powerful and reliable method to solve any quadratic equation. Just follow the steps:

• Identify a, b, and c
• Plug them into the formula
• Simplify carefully
• Interpret the results!

Hope you can solve quadratic equation using formula method easily? Share and comment on our comment section below.