medium importancemedium difficulty7 min

Equation reduction from context

Equation reduction means converting a formed relation into a simpler quadratic equation in standard form by expanding and rearranging terms.

In one line: Expand, shift, and finish with zero.

Practice This Concept

Understand it

After a word problem is translated into algebra, the equation often needs expansion and simplification. The final step is to move every term to one side so the equation becomes ax² + bx + c = 0.

Example

From x(x + 7) = 18, we get x² + 7x - 18 = 0.

Formula and rule

Expand the relation, collect like terms, and write the result in the form ax² + bx + c = 0.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

Start with x(x + 5) = 24.

1Expand to x² + 5x = 24.
2Move 24 to the left side to get x² + 5x - 24 = 0.
3Now the equation is ready for solving.

Method you can reuse

1Expand the given relation.
2Collect all terms on one side.
3Keep zero on the other side.
4Check the highest power is 2.

Visual tip

A three-step arrow diagram works well: relation → expansion → standard form.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What is the correct reduced form of x(x + 5) = 24?

Think first, then show answer

It becomes x² + 5x - 24 = 0. First expand x(x + 5), then bring 24 to the left side.

Common wrong answer

Writing x² + 5x = 24 as the final answer is incomplete because it is not in standard form.

Don't mix this up

Students often stop after expansion and forget to bring the constant term to the left side.

Exam tip

Always end the reduction step with '= 0', because standard form makes solving easier.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

CBSE may ask for the equation after reducing a word relation or may give the expanded form and ask for the standard form.

1
Enough for 1 mark
Equation reduction means converting a formed relation into a simpler quadratic equation in standard form by expanding and rearranging terms.
2
Add for 2 marks
Example: From x(x + 7) = 18, we get x² + 7x - 18 = 0.
3
Add for 3 marks
After a word problem is translated into algebra, the equation often needs expansion and simplification.

MCQ Quiz

Practice this concept with focused MCQs

Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.

10 MCQs5 MinutesInstant Results