Problems involving Quadratic Equations

We want a rectangular sign with an area of 25m² for our business. The length of the sign is to be 4m longer than the width. What will be the length and width of the sign?

let x = width

let x + 4 = length

then x(x + 4) = 25 using the formula for AREA of a rectangle.

x(x + 4) = 25

x² + 4x = 25

1. Complete the square:

x² + 4x + 4 = 25 + 4

(x + 2)²  = 25 + 4

x + 2 = ±√29
x  = -2 ±√29

-2 ±√29 ≅ 3.4, we discard the negative square root since lengths can't be negative.

3.4(3.4+4) = 25
3.4(7.4) = 25
25.16 ≅ 25

The height of our sign is 3.4m and the width is 7.4m.

Transforming Formulas

Formulas are used in alot of mathematical applications. It is very often useful to transform a formula in order to express a particular variable in terms of the other variables.









For example, in the formula for piston displacement of an automobile engine:

P = 0.7854d^2sn

 to solve for s in terms of P, n, and d this formula can be rewritten

P/0.7854d^2n = s.