The product of two positive numbers is 84. The larger number is 2 more than twice the smaller number. What is the larger number?

44. (Sorry if im incorrect. I don't clearly understand the question)

Step-by-step explanation:

14 or -12

Step-by-step explanation:

Start by writing an equation for this.

84 = x * (2x + 2)

This expression works because 84 is the product of the number (x) and twice the number plus 2.

Using the equation, solve for x.

84 = x * (2x + 2)

First, simplify.

84 = 2x^2 + 2x

Subtract 2x^2 + 2x to make the equation equal to 0.

84 - 2x^2 + 2x = 0

Factor:

−2(x − 6)(x + 7) = 0

Set factors equal to 0.

x − 6 = 0 or x + 7 = 0

x = 6 or x = -7

x represents the smaller number. The larger number is 2x + 2.

So double x and add 2.

2(6) = 12 and 12 + 2 = 14 so that's one of the options

2(-7) = -14 and -14 + 2 = -12 so that's the other.

Check:

14 * 6 = 84

-12 * -7 = 84