Calculate x in Rectangular Area Equation: 2(x-4) by 2x+8 Yields 132

To solve the problem, let's proceed with the following steps:

• Step 1: Identify the area formula
• Step 2: Substitute side expressions
• Step 3: Simplify the equation and solve

Let's begin:
Step 1: The area of the rectangle is given by the formula:
$\text{Area} = \text{Length} \times \text{Width}$ For this rectangle, the length and width are given as $2x + 8$ and $2(x-4)$, respectively. Thus, we have the equation for the area:

$(2x + 8) \times (2(x - 4)) = 132$

Step 2: Substitute the side expressions and set up the equation:

$(2x + 8) \times (2x - 8) = 132$

Step 3: Expand and solve:

• First, we expand the expression using multiplication:
• The side expression simplifies to a difference of squares:

$(2x + 8)(2x - 8) = (2x)^2 - 8^2$ $= 4x^2 - 64$

The area equation is:

$4x^2 - 64 = 132$

Step 4: Simplify and solve the quadratic equation:

• Add $64$ to both sides to isolate the quadratic term:
$4x^2 = 196$
• Divide by $4$:
$x^2 = 49$
• Take the square root:
$x = \pm \sqrt{49}$ $x = \pm 7$

Therefore, the solutions for $x$ are $x = 7$ and $x = -7$. Since area is scalar, both positive and negative solutions are valid for $x$.

Thus, the correct value for $x$ is $\pm 7$.