Solve for x in the Parallelogram Area Equation: (x+3)(x-3)

Question

The area of the parallelogram is equal to (x+3)(x3) (x+3)(x-3) .

Calculate x.

999333

Video Solution

Solution Steps

00:00 Find X
00:03 We'll use the formula for calculating the area of a parallelogram (base times height)
00:15 We'll substitute appropriate values according to the given data and solve for the area
00:23 This is the area of the parallelogram
00:28 We'll substitute the parallelogram's area in the equation and solve for X
00:39 We'll use the shortened multiplication formulas to expand the brackets
00:55 Calculate 3 squared
01:00 Isolate X
01:10 Take the square root to find possible solutions for X
01:20 And this is the solution to the problem

Step-by-Step Solution

The problem requires calculating the value of x x from the expression given for the area of a parallelogram: (x+3)(x3) (x+3)(x-3) .

Recognize that the expression (x+3)(x3) (x+3)(x-3) can be expanded using the identity for the difference of squares:

(x+3)(x3)=x232 (x+3)(x-3) = x^2 - 3^2

Thus, it simplifies to:

x29 x^2 - 9

Understanding from the problem that this represents the area of the parallelogram, and after setting it equal to zero:

x29=0 x^2 - 9 = 0

To solve for x x , add 9 to both sides to isolate x2 x^2 :

x2=9 x^2 = 9

Take the square root of both sides, remembering that squaring gives two solutions:

x=±9=±3 x = \pm \sqrt{9} = \pm 3

Thus, the solutions for x x are x=3 x = 3 and x=3 x = -3 .

Therefore, the value of x x is ±6\pm6.

Therefore, the solution to the problem is x=±3 x = \pm3 .

Answer

±6 \pm6