Solve for X: Calculating the Area of a Rectangle with (x-7)(x+7)

To find $x$, we'll begin by calculating the area of the rectangle using its dimensions:

• Step 1: Calculate the area $A$ using the dimensions 5 and 19:
  $A = 5 \times 19 = 95$
• Step 2: Set up the equation using the difference of squares:
  $(x-7)(x+7) = x^2 - 49$
• Step 3: Equate to the area calculated:
  $x^2 - 49 = 95$
• Step 4: Solve for $x^2$:
  $x^2 = 95 + 49 = 144$
• Step 5: Solve for $x$ by taking the square root:
  $x = \pm \sqrt{144} = \pm 12$

Therefore, the solutions for $x$ are $x = \pm 12$.