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

A train 150 m long passes a pole in 15 seconds. What is its speed?

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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What is the value of log₃(27)?

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If x^2 - 6x + 9 = 0, what is the value of x?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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What is the sum of all even numbers between 1 and 50?

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If a = 4 and b = 5, what is the value of (a+b)^2?

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If 8x = 512, what is the value of x?

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If a:b = 3:4 and b:c = 5:6, what is a:c?

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

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