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Updated Mar 19, 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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Updated Mar 19, 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!

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

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.