**Uncut piece of cardboard:**

**Width: x inches**

**Length: 2x inches**

**Piece of cardboard with four cut-out corners:**

**Subtract 2 × 2 inches from length and width to compute for the volume of the box.**

**Width: x - 4 inches**

**Length: 2x - 4 inches**

**Height: 2 inches**

**Volume: 140 cubic inches**

**Equation:**

**Length × Width × Height = Volume**

**(2x-4) (x - 4) (2) = 140**

**(2x² - 8x - 4x + 16) (2) = 140**

**(2x² - 12x + 16) (2) = 140**

**4x² - 24x + 32 = 140**

**Quadratic equation, ax² + bx + c = 0**

**4x² - 24x + 32 - 140 = 0**

**4x² - 24 - 108 = 0**

**Solve by factoring:**

**4 (x² - 6x - 27) = 0**

**4 (x - 9) (x + 3) = 0**

**x - 9 = 0 x + 3 = 0**

__x = 9__ x = -3

**Choose the positive root x = 9.**

**The dimensions of the piece of cardboard (uncut) are:**

**Width: x = **__9 inches__

**Length: 2x = 2(9) =** **18 inches**

The dimensions are 9 inches and 18 inches.

**Check:**

**(18-4) (9-4) (2) = 140**

(14) (5) (2) = 140

140 = 140