SOLUTION: Please help solve: Show all work: The area of a rectangular swimming pool is given by 2x^2+x-10ft^2. One side length of the pool is given by 2x+5 ft. What is an algebric express

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help solve: Show all work: The area of a rectangular swimming pool is given by 2x^2+x-10ft^2. One side length of the pool is given by 2x+5 ft. What is an algebric express      Log On


   

Question 404597: Please help solve:
Show all work: The area of a rectangular swimming pool is given by 2x^2+x-10ft^2. One side length of the pool is given by 2x+5 ft. What is an algebric expression for the length of the pool? Simplify and include correct units.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The area A of a rectangular swimming pool is given by 2x%5E2%2Bx-10ft%5E2.
so, you have:
A+=+%282x%5E2%2Bx-10%29ft%5E2
One side length a of the pool is given by %282x%2B5%29ft....so, we have
a+=+%282x%2B5%29ft

What is an algebraic expression for the length of the pool b?
Simplify and include correct units.

we know that:

A+=+ab

b+=+A%2Fa...now substitute A+=+%282x%5E2%2Bx-10%29ft%5E2 and a+=+%282x%2B5%29ft

b+=+%282x%5E2%2Bx-10%29ft%5E2%2F%282x%2B5%29ft....simplify...replace 1x with -4x+%2B5x

b+=+%282x%5E2+-4x+%2B5x-10%29ft%5Ecross%282%291%2F%282x%2B5%29cross%28ft%29...group

b+=+%28%282x%5E2+-4x%29+%2B%285x-10%29%29ft%2F%282x%2B5%29

b+=+%282x%28x+-2%29+%2B5%28x-2%29%29ft%2F%282x%2B5%29

b+=+%28%282x%2B5%29%28x-2%29%29ft%2F%282x%2B5%29

b+=+%28cross%28%282x%2B5%29%29%28x-2%29%29ft%2Fcross%28%282x%2B5%29%29

b+=+%28x-2%29ft