Let's go through the steps to solve the problem shown in the first image. The problem seems to be based on a rectangular flower bed and some unknown values that need to be found.

Image 1: Step-by-step breakdown:

Step 1: Translate the situation into a quadratic equation.

• We are given a rectangular flower bed with the following dimensions:

  • Width of the flower bed: 8 meters
  • Length of the flower bed: 10 meters

  There is a walking path (道) around the flower bed that is of a uniform width, and the total area of the flower bed plus the path is 48 square meters.

Let the unknown width of the path be represented by x meters.

• The total dimensions of the flower bed plus the path will then be:
  • Length: $10 + 2x$ meters (since there is a path on both sides, the total length increases by $2x$).
  • Width: $8 + 2x$ meters (similarly, the width increases by $2x$).

The total area, including the path, is given as 48 square meters.

Step 2: Form a quadratic equation.

The area of the flower bed plus the path is the product of the length and width, and we know it equals 48 square meters:

$(10 + 2x)(8 + 2x) = 48$

Now, expand the equation:

$(10 + 2x)(8 + 2x) = 80 + 20x + 16x + 4x^2 = 80 + 36x + 4x^2$

Set the equation equal to 48:

$80 + 36x + 4x^2 = 48$

Subtract 48 from both sides:

$4x^2 + 36x + 32 = 0$

Step 3: Solve the quadratic equation.

We now have a quadratic equation:

$4x^2 + 36x + 32 = 0$

First, divide through by 4 to simplify:

$x^2 + 9x + 8 = 0$

Now, solve using the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

For this equation, (a