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Equation reduction from context

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

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Student-friendly explanation

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 ax^2 + bx + c = 0.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

    From x(x + 7) = 18, we get x^2 + 7x - 18 = 0.

  4. 4

    Avoid this incomplete answer

    Writing x^2 + 5x = 24 as the final answer is incomplete because it is not in standard form.

Definition

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

Example

From x(x + 7) = 18, we get x^2 + 7x - 18 = 0.

Rule to remember

Expand the relation, collect like terms, and write the result in the form ax^2 + bx + c = 0.

Sequence to remember

Expand the relation, collect like terms, and write the result in the form ax^2 + bx + c = 0. A three-step arrow diagram works well: relation>
expansion>
standard form. 1. Expand the given relation. 2. Collect all terms on one side. 3. Keep zero on the other side. 4. Check the highest power is 2

Memory hook

Expand, shift, and finish with zero.

Examples and method

Worked example

Start with x(x + 5) = 24. Expand to x^2 + 5x = 24. Move 24 to the left side to get x^2 + 5x - 24 = 0. Now the equation is ready for solving.

Method to apply

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

Diagram support

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

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.

Avoid common mistakes

Common confusion

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

Common wrong answer

Writing x^2 + 5x = 24 as the final answer is incomplete because it is not in standard form.

Exam tip

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

Quick check

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

It becomes x^2 + 5x - 24 = 0. First expand x(x + 5), then bring 24 to the left side.

Answer writing and exam use

1-mark answer

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

2-mark answer

Equation reduction means converting a formed relation into a simpler quadratic equation in standard form by expanding and rearranging terms. Expand the relation, collect like terms, and write the result in the form ax^2 + bx + c = 0. From x(x + 7) = 18, we get x^2 + 7x - 18 = 0.

3-mark answer

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 ax^2 + bx + c = 0. Expand the relation, collect like terms, and write the result in the form ax^2 + bx + c = 0. Start with x(x + 5) = 24. Expand to x^2 + 5x = 24. Move 24 to the left side to get x^2 + 5x - 24 = 0. Now the equation is ready for solving. CBSE may ask for the equation after reducing a word relation or may give the expanded form and ask for the standard form. Writing x^2 + 5x = 24 as the final answer is incomplete because it is not in standard form.
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