To determine the width of the strip, we need to solve the equation
(44-2x)(32*2x) = 704m^2
First, let's simplify both sides of the equation.
(44-2x)(32*2x) = 704
(44-2x)(64x) = 704
2816x - 128x^2 = 704
Rearranging the equation to a quadratic form:
128x^2 - 2816x + 704 = 0
Dividing the entire equation by 16 to simplify:
8x^2 - 176x + 44 = 0
Now, let's solve this quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 8, b = -176, and c = 44.
x = (-(-176) ± √((-176)^2 - 4*8*44)) / (2*8)
x = (176 ± √(30976 - 1408)) / 16
x = (176 ± √(29568)) / 16
x = (176 ± √(736*4*4)) / 16
x = (176 ± (4√(184))) / 16
x = (44 ± √(184)) / 4
Therefore, the potential solutions for the width of the strip are:
x = (44 + √(184)) / 4 and x = (44 - √(184)) / 4
These are the two possible values for the width of the strip that would result in each laborer mowing the same area.
Determine the width of the strip so that each labourer mows the same area using this equation
(44-2x)(32*2x)= 704m^2
1 answer
1 answer