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

The area of the rectangle below is equal to $(x-7)(x+7)$ .

Calculate x.

Video Solution

Solution Steps

00:00 Find X

00:03 We'll use the formula for calculating rectangle area (side times side)

00:10 We'll substitute appropriate values according to the given data and solve for the area

00:13 This is the rectangle's area

00:17 We'll substitute the rectangle's area in the equation and solve for X

00:28 We'll use the square of binomials formula to expand the brackets

00:47 Calculate 7 squared

00:56 Isolate X

01:09 Take the square root to find possible solutions for X

01:14 And this is the solution to the problem

Step-by-Step Solution

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 $x = \pm 12$ .