SOLUTION: the length of a rectangular flower garden in (x-7) and the width is (x+5). If the area is 28 sq meters, find the value of x.

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Question 595780: the length of a rectangular flower garden in (x-7) and the width is (x+5). If the area is 28 sq meters, find the value of x.
Answer by llorton(14) (Show Source):
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length * width = area
(x-7)(x+5) = 28 (multiply length times width)
x^2 - 2x - 35 = 28
x^2 - 2x - 35 - 26 = 28 - 28 (Subtract 28 from each side of the equation)
x^2 - 2x - 63 = 0
(x - 9)(x + 7) = 0 (factor the quadratic by inspection)
x - 9 = 0
x = 9 (Since we are talking about a flower bed, the
positive value is all we are interested in.)
x + 7 = 0
x = -7
We can check our answer by substituting x = 9 in the equations for length and width. l=9-7=2; w=9+5=14; area=2*14=28