The area of a rectangle is 8cm^2. It has a length of (3x+1)cm and a width of (2x+5)cm. Work out the value of x.

We know that the equation of the area of a rectangle is width times by length. Therefore:

8=(3x+1)(2x+5)

If we multiply out the brackets we get:

8=(6x²+2x+15x+5), thus, 8=6x²+17x+5, and therefore, 0=6x²+17x-3

One technique that I found useful to find the value of x when the coefficient of x² is greater than one is to split the coefficient of x. Therefore we must find 2 numbers that when multiplied equal (-18) and add to 17. The answer to this is 18 and (-1).

Thus we get, 0=6x²+18x-x-3. We can then factorise this equation to 0=6x(x+3)-1(x+3), and then 0=(6x-1)(x+3). This means that we get 2 answers to this quadratic - when 6x-1=0 and x+3=0.

Thus x=1/6 and -3. As x cannot be negetive, the answer is 1/6.