> ## Content Index
> Fetch the complete content index at: https://www.esheets.io/llms.txt
> Use this file to discover other available public pages before exploring further.

# Quadratic formula - decimal solutions
- URL: https://www.esheets.io/quadratic-formula-decimal-solutions/
- Published: 2025-06-02T19:10:39.000Z
- Updated: 2026-06-21T17:02:06.000Z
- Author: Richard Linnington
- Tags: Maths, Algebra

You’ll often see the quadratic formula when trying to solve equations where something is squared – such as in physics when calculating the path of a thrown object, or in engineering when designing curves. It’s a powerful tool that always works, even when factorising doesn’t! [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise using the quadratic formula to find decimal solutions with this self-marking maths worksheet.

The interactive worksheet below generates questions, gives instant feedback, and lets students record their score.

#### What you’ll practise

- Identifying a, b and c.
- Substituting into the quadratic formula.
- Calculating both solutions.
- Rounding decimal solutions appropriately.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

Solve each equation and round both solutions to 1 decimal place.

  
## Topic guide

### What this worksheet practises

This worksheet focuses on using the Quadratic Formula to solve complex quadratic equations (ax² + bx + c = 0) that cannot be factorised. This is a calculator-heavy topic where precision is absolutely vital.

### Key method

You must substitute your values carefully into the formula: **x = (−b ± √(b² − 4ac)) / 2a**

- Identify the values for **a** (the number attached to x²), **b** (the number attached to x), and **c** (the number on its own). Ensure the equation equals zero first.
- Calculate the "discriminant" first: **b² − 4ac**. This is the part that lives inside the square root. Calculating this first drastically reduces calculator errors.
- Substitute everything into the main formula.
- Because of the ± symbol, you must do the final calculation twice: once using a plus sign, and once using a minus sign. This gives you two distinct answers.

### Worked example

**Solve 2x² + 5x − 4 = 0 to 2 decimal places.**

Step 1: Identify a, b, and c.

a = 2, b = 5, c = −4.

Step 2: Calculate the discriminant (b² − 4ac).

(5)² − (4 × 2 × −4)

25 − (−32)

25 + 32 = 57.

Step 3: Put it all into the main formula.

x = (−5 ± √57) / (2 × 2)

x = (−5 ± √57) / 4

Step 4: Calculate the two answers using your calculator.

Plus version: x = (−5 + √57) / 4 = 0.6374...

Minus version: x = (−5 − √57) / 4 = −3.1374...

Step 5: Round to 2 decimal places.

x = 0.64 or x = −3.14.

### Common mistakes to avoid

The single most dangerous error involves negative numbers in the discriminant, specifically when squaring a negative 'b'. If b = −3, typing -3² into a calculator gives −9\. You must type (−3)² to get the correct answer of +9\. A squared number in the formula must always be positive.

### How to check your answer

You can verify your answers by substituting them back into the original equation. For example, 2(0.64)² + 5(0.64) − 4\. This calculation will equal 0.0192\. Because it is extremely close to zero, it proves our rounded answer of 0.64 is correct.