The area of a rectangle is represented by the equation w^2 + 4w = 60 where w the width of the rectangle. Find the width.

Answer 1

W² + 4W = 60.

Equations to 2nd power are called quadratics. Simple ones like this can be solved by factoring. More difficult ones need a formula call the Quadratic Formula.

To solve by factoring, first bring all terms to one side:

W² + 4W - 60 = 0. Now to solve this by factoring need to find two numbers a, b so that they multiply to -60 and add to 4:

a * b = -60

and

a + b = 4

The two numbers that work are 10 and -6:

(10) * (-6) = -60

and

(10) + (-6) = 4

After you find the two numbers a, b they are used to factor the quadratic like this:

W² + 4W - 60 = (W - 6)(W +10) = 0

Finally, set each factor separately equal to 0 and solve each separately:

W - 6 = 0 ———-> W = 6

W +10 = 0 ———> W = -10

But since this supposed to be a width, we choose the positive answer 6.