**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 uncovered box formed.**

**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 + bc + c = 0**

**4x² - 24x + 32 - 140 = 0**

**4x² - 24x - 108 = 0**

**Solve by factoring:**

**4(x² - 6x - 27) = 0**

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

__x = 9 __ x = -3

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

**Dimensions of the uncut piece of board:**

**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**