A rectangular vegetable garden will have a width that is 4 feet less than the length, and an area of 140 square feet. If x represents the length, then the length can be found by solving the equation: x(x-4)=140 What is the length,x, of the garden? The length is __ feet. The solution is square

## Step 1: Set up the equation### The problem states that the width is 4 feet less than the length, and the area of the rectangle is given by the formula for the area of a rectangle, which is length times width. Therefore, we have the equation \( x(x-4) = 140 \).## Step 2: Solve the quadratic equation### Expand the equation to get . Rearrange it to form a standard quadratic equation: .## Step 3: Factor the quadratic equation### To factor the quadratic equation, find two numbers that multiply to -140 and add to -4. These numbers are -14 and 10. Thus, the equation factors as \( (x - 14)(x + 10) = 0 \).## Step 4: Solve for x### Set each factor equal to zero: or . Solving these gives or .## Step 5: Determine the valid solution### Since length cannot be negative, the valid solution is .