In the following equation, identify the x-intercepts in the graph y = 3x2 + 19x – 40The dimensions of Eric’s pool are 9 feet by 7 feet. He wants to build a walkway surrounding the pool so that the square footage of the walkway and pool is 143 square feet. How wide is one side of the walkway?

Question

In the following equation, identify the x-intercepts in the graph y = 3x2 + 19x – 40The dimensions of Eric’s pool are 9 feet by 7 feet.  He wants to build a walkway surrounding the pool so that the square footage of the walkway and pool is 143 square feet. How wide is one side of the walkway?

anonymous · Answer

@greenlegodude57

anonymous · Answer

Let x = the width of the pool 
Since the walkway goes all the way around the pool the over dimensions will be: 
(2x+9) by (2x+7); then the overall area (pool & walkway) will be: 
(2x+9)*(2x+7) = 143 
FOIL 
4x^2 + 14x + 18x + 63 = 143 
4x^2 + 32x + 63 - 143 = 0 
4x^2 + 32x - 80 = 0; quadratic equation 
Simplify, divide by 4 
x^2 + 8x - 20 = 0 
Factors to 
(x+10)(x-2) = 0 
The positive solution is what we want here 
x = 2 ft is the width of the walkway