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

If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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If a rectangle has a length of 10 cm and a width of 6 cm, what is its perimeter?

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

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A sum of money doubles itself in 5 years at simple interest. What is the rate of interest?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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