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💡 What is a Quadratic Equation?
A quadratic equation is a second-degree polynomial equation that looks like this:
ax² + bx + c = 0
Where:
a, b, and c are constants
x is the variable
a ≠ 0
Examples:
2x² - 7x + 3 = 0
a = 2, b = -7, c = 3
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🚀 Step-by-Step Method: The Quadratic Formula
The easiest universal way to solve quadratic equations is using this formula:
x = (-b ± √(b² - 4ac)) / (2a)
This is called as Quadratic Formula
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✅ Step 1: Identify a, b, and c
Look at your equation and match the terms.
Example:
2x² - 7x + 3 = 0
Here:
a=2
b=-7
c=3
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✅ Step 2: Plug into the Formula
Use:
x = (-b ± √(b² - 4ac)) / (2a)
Substitute the values:
x = (-(-7) ± √((-7)² - 4 × 2 × 3)) / (2 × 2)
x = (7 ± √(49 - 24)) / 4
x = (7 ± √25) / 4
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✅ Step 3: Solve
x = (7 + 5) / 4 = 12 / 4 = 3
x = (7 - 5) / 4 = 2 / 4 = 0.5
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🎉Final Answer
x=3
or
x=0.5
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🧠 Bonus: What’s That Square Root Part?
This part of the formula:
√(b² - 4ac)
is called the discriminant (usually written as D). It tells you how many and what kind of solutions the equation has.
Discriminant(D) What It Means
D>0 Two real solutions
D=0 One real solution(repeated)
D<0 No real solutions (imaginary roots)
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🎯 Final Thoughts
Quadratic equations don’t have to be hard. Just follow these 3 steps:
1. Identify a, b, and c
2. Plug them into the formula
3. Simplify and solve
And you’re done!
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