The area of a rectangular knitted blanket is 14x^2-17x-6. What are the possible dimensions of the blanket? Use factoring.

Solve for x using factoring:

14 x^2 - 17 x - 6 = 0

The left hand side factors into a product with two terms:

(2 x - 3) (7 x + 2) = 0

Split into two equations:

2 x - 3 = 0 or 7 x + 2 = 0

Add 3 to both sides:

2 x = 3 or 7 x + 2 = 0

Divide both sides by 2:

x = 3/2 or 7 x + 2 = 0

Subtract 2 from both sides:

x = 3/2 or 7 x = - 2

Divide both sides by 7:

Answer: x = 3/2 or x = - 2/7