Question

Trevor is building a deck. He has enough wood to build a 15 ft2 deck. Trevor wants

the deck to be 2 ft longer than it is wide. He sets up the following equations to
help him determine the dimensions of the deck.

x(x + 2) =15
x + 2x -15 =0
where xis the width of the deck in feet.

How wide should Trevor make his deck? To solve for x, first factor the
left side of the equation. Note: The width of the deck must be positive.
Ignore negative values for x.

Answer 1

The deck width is 3

Explanation:

Your

x(x + 2) =15

x + 2x -15 =0

should be:

x(x + 2) =15

x^2 + 2x -15 =0.

Factoring this, we get

x^2 + 2x -15 =0 = (x + 5)(x - 3) = 0,

which yields: x = 3 and x = -5. As the problem states, we discard the negative root and focus on the positive one (x = 3).

The deck width is 3 and the length is (3 + 2), or 5.