We employ the following general problem solving method, when solving worded problems involving quadratic equations.

- Define the terms if required.
- Convert the sentences or sentence parts into algebraic terms.
- Look for keywords such as equal, subtracted from, multiplied by ... and so on.
- Write an equation in the form $ax^2+bx+c=0$ form.
- Solve the equation by factorising, completing the square or quadratic formula.
- Decide which solutions are valid
- Answer the question in a sentence.

- if we are finding a length it must be positive and we reject any negative solutions.
- if we are finding 'how many people are present' then clearly the answer must be an integer.

### Example 1

A rectangle has length $4$ cm longer than its width. If the area is $45$ cm^{2}. Find its width.