Topic Details (Notes format)

How to Use Completing the Square Technique

Subject: Mathematics

Book: Maths Mastery

Completing the square rewrites a quadratic ax² + bx + c into a(x – h)² + k form. For instance, x² + 6x + 5 → (x² + 6x + 9) – 9 + 5 → (x + 3)² – 4. This reveals the vertex or allows direct factoring. It’s also vital in derivations (quadratic formula), geometry (circle equations), and calculus (integrals of certain forms). Mastering it fosters deeper insight into parabola properties and simplifies many otherwise cumbersome algebraic tasks.

Practice Questions

What is the value of x if 3x + 7 = 16?

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The probability of rolling a sum of 7 with two dice is:

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A cube has a side length of 4 cm. What is its volume?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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What is the cube root of 729?

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The area of an equilateral triangle with side length 6 cm is:

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If a number is divisible by 9, it is also divisible by which of the following?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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The LCM of 12 and 15 is:

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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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