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

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To solve for the dimensions of a rectangle given the force exerted by air, the equation F = 10^5A is used, leading to A = 10 square meters. The dimensions are defined as length (L) being 2 meters longer than width (w), resulting in the equation 10 = (2 + w)w. This simplifies to the quadratic equation w^2 + 2w - 10 = 0. The quadratic formula or completing the square can be applied to find the width, which will then allow the calculation of the length. The solution process involves standard quadratic solving techniques to determine the rectangle's dimensions.
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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.
 
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Its a quadratic. Could use the quadratic formula
 
so what i did was corrent, i just got to use the quadradic formula and that's it yeh?
 
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.
 
Starting from w2+ 2w= 10, completing the square leaps to mind!
 

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