How Do You Solve a Quadratic Equation to Find Dimensions of a Rectangle?

[i-love-physics]

Homework Statement

The force (in Newtons) that air exerts on a surface is given by the formula
F = 10^5A

Where A is the surface area (in square metres). Suppose that the air supplies 10^6 Newtons of force on a rectangular surface that is 2 metres longer than it is wide. Find the dimensions (to 2 decimal place) of the rectangular surface.

Homework Equations

The Attempt at a Solution

This is my attempt

10^6 = 10^5A
A= 10

10 = LW
10 = (2+w)w
10= 2w +w^2

now i am stuck here..

If anyone knows what to do it would be greatly appreciated if you could help me out, thank you.

 

[danago]

Its a quadratic. Could use the quadratic formula

 

[i-love-physics]

so what i did was corrent, i just got to use the quadradic formula and that's it yeh?

 

[danago]

As far as I am aware, yes.

For a quadratic like that, the first thing i would do is write it as:

w²+2w-10=0

And see if i can write it in the form (x+a)(x+b)=0. If not, then id probably proceed to use the quadratic formula.

 

[HallsofIvy]

Starting from w²+ 2w= 10, completing the square leaps to mind!