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\"\"

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The general form of quadratic equation is \"\".

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The width of the rectangular shape of floor is w feet and its length(l) is w + 14 feet.

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The area of the rectangular formula is \"\".

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The area of the rectangular shape of floor is \"\" = 1632.

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\"\"                                       (Substitute \"\")

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\"\"                                        (Apply distributive property: \"\")

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\"\"               (Subtract 1632 from each side)

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\"\"                                  (Apply additive inverse property: \"\")\"\"

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The quadratic equation for area of the floor is \"\".

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\"\"

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The width of the rectangular shape of floor is  w feet and its length is w + 14 feet.

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The rectangular area formula is \"\".

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The area of the rectangular shape of floor is \"\".

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\"\"                                (Substitute \"\")

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\"\"                                 (Apply distributive property: \"\")

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\"\"        (Subtract 1632 from each side)

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\"\"                           (Apply additive inverse property: \"\")\"\"

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The quadratic equation is \"\" in w - variable.

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The general form of quadratic equation is \"\" in x - variable.

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The quadratic formula  \"\".

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\"\"  (Substitute \"\")

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\"\"                                 (Simplify)

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\"\"                                         (Simplify)

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\"\"            (First solution)

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\"\"     (Second solution)

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The value of dimension (width) is always positive, so consider value of w = 34 feet. \"\"

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The width of the floor is w = 34 feet and its length is w + 14 feet.

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The length of the floor = w + 14 = 34+14 = 48 feet      (Substitute w = 34)\"\"

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The width of the floor is 34 feet and its length is 48 feet.