Question

The area of a rectangular swimming pool is 10x2 – 19x – 15. The length of the pool is 5x + 3. What is the width of the pool?

Answer 1

Area = length * width. so
10x*2 - 19x - 15 = 5x + 3 * w

Answer 2

or 10x*2 - 19x - 15 = 5x + 3 * x
Simplifying
10x * 2 + -19x + -15 = 5x + 3x

Reorder the terms for easier multiplication:
10 * 2x + -19x + -15 = 5x + 3x

Multiply 10 * 2
20x + -19x + -15 = 5x + 3x

Reorder the terms:
-15 + 20x + -19x = 5x + 3x

Combine like terms: 20x + -19x = 1x
-15 + 1x = 5x + 3x

Combine like terms: 5x + 3x = 8x
-15 + 1x = 8x

Solving
-15 + 1x = 8x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-8x' to each side of the equation.
-15 + 1x + -8x = 8x + -8x

Combine like terms: 1x + -8x = -7x
-15 + -7x = 8x + -8x

Combine like terms: 8x + -8x = 0
-15 + -7x = 0

Add '15' to each side of the equation.
-15 + 15 + -7x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -7x = 0 + 15
-7x = 0 + 15

Combine like terms: 0 + 15 = 15
-7x = 15

Divide each side by '-7'.
x = -2.142857143

Simplifying
x = -2.142857143

Answer 3

drkole's set up was correct but the work is incorrect.
the missing width is (2x-5)
because length times width = Area
(5x+3)(2x-5)=10x^2-19x-15

Answer 4

Thank you!

Answer 5

Anytime :)