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13 Jan 2026

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2 pages

Understanding Quadratic Equations: Key Concepts Explained

laila

@la1la

Ready to tackle quadratic equations? They might look scary at... Show more

1/11/22
Lo: to be able to solve quadratic equations
starter:
1 factorise!
$x^2+7x+12:$
(x+3) (x+4)
factor pairs: + 12
1
+12
2
6
3
4
2$x^2-12

Getting Started with Quadratic Equations

Think of quadratic equations as puzzles that need breaking down into smaller pieces. When you see something like x² + 7x + 12, your job is to split it into two brackets that multiply together.

The key trick is finding factor pairs - numbers that multiply to give you the constant term (the number without x). For x² + 7x + 12, you need pairs that multiply to give 12 and add to give 7. That's where 3 and 4 come in perfectly!

Once you've got your brackets like $x + 3$ $x + 4$ = 0, solving becomes dead easy. If two things multiply to give zero, one of them must be zero. So either x + 3 = 0 $making x = -3$ or x + 4 = 0 $making x = -4$ .

Quick Tip: Always check your factor pairs add up to the middle coefficient - it's your safety net!

Mastering Different Types of Quadratics

Not all quadratics are the same, but the method stays consistent. Whether you're dealing with x² + 8x + 7 = 0 or x² + 10x - 11 = 0, you're still hunting for those magic factor pairs.

Notice how the second example has a negative constant term (-11)? This means one factor will be positive and one negative. For -11, you need 1 and -11, which gives you $x - 1$ $x + 11$ = 0.

Setting each bracket to zero gives you your solutions: x = 1 and x = -11. Easy as that! The beauty of factorising quadratics is that once you've cracked the pattern, every equation follows the same logic.

Remember: When the constant is negative, your factors will have opposite signs - one plus, one minus.

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13 Jan 2026

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2 pages

Understanding Quadratic Equations: Key Concepts Explained

laila

@la1la

Ready to tackle quadratic equations? They might look scary at first, but once you get the hang of factorising, you'll be solving them like a pro! This lesson shows you step-by-step how to break down quadratics and find their solutions.

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Getting Started with Quadratic Equations

Think of quadratic equations as puzzles that need breaking down into smaller pieces. When you see something like x² + 7x + 12, your job is to split it into two brackets that multiply together.

Quick Tip: Always check your factor pairs add up to the middle coefficient - it's your safety net!

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Mastering Different Types of Quadratics

Not all quadratics are the same, but the method stays consistent. Whether you're dealing with x² + 8x + 7 = 0 or x² + 10x - 11 = 0, you're still hunting for those magic factor pairs.

Notice how the second example has a negative constant term (-11)? This means one factor will be positive and one negative. For -11, you need 1 and -11, which gives you $x - 1$ $x + 11$ = 0.

Remember: When the constant is negative, your factors will have opposite signs - one plus, one minus.