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<br />### 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 \( x(x-4) = 140 \).<br />## Step 2: Solve the quadratic equation<br />### Expand the equation to get \( x^2 - 4x = 140 \). Rearrange it to form a standard quadratic equation: \( x^2 - 4x - 140 = 0 \).<br />## Step 3: Factor the quadratic equation<br />### 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 \( (x - 14)(x + 10) = 0 \).<br />## Step 4: Solve for x<br />### Set each factor equal to zero: \( x - 14 = 0 \) or \( x + 10 = 0 \). Solving these gives \( x = 14 \) or \( x = -10 \).<br />## Step 5: Determine the valid solution<br />### Since length cannot be negative, the valid solution is \( x = 14 \).