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 the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

The simple interest on Rs. 4000 at 5% per annum for 2 years is:

If a+b = 10 and ab = 21, what is the value of (a-b)^2?

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

What is the value of x if log(x) + log(4) = log(32)?

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

What is the sum of all even numbers between 1 and 100?

If x:y = 4:5 and y:z = 2:3, what is x:z?

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

What is the area of a sector of a circle with radius 14 cm and central angle 90°?