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Quadratic Formula

Solve each of...

Question

Solve each of the following equation:

$(x^{2} + 5 x + 4) (x^{2} + 5 x + 6) = 120$

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Solution

$left parenthesis x squared plus 5 x plus 4 right parenthesis left parenthesis x squared plus 5 x plus 6 right parenthesis equals 120 L e t space space x squared plus 5 x equals y t h e n space left parenthesis y plus 4 right parenthesis left parenthesis y plus 6 right parenthesis equals 120 y squared plus 6 y plus 4 y plus 24 minus 120 equals 0 y squared plus 10 y minus 96 equals 0 y squared plus 16 y minus 6 y minus 96 equals 0 y left parenthesis y plus 16 right parenthesis minus 6 left parenthesis y plus 16 right parenthesis equals 0 left parenthesis y plus 16 right parenthesis left parenthesis y minus 6 right parenthesis equals 0 y equals negative 16 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space o r space space space space y equals 6 x squared plus 5 x plus 16 equals 0 space space space space space space space space space space space space space space space space space space space space space space space space space space o r space space space x squared plus 5 x minus 6 equals 0 x equals fraction numerator negative 5 plus-or-minus square root of left parenthesis 5 right parenthesis squared minus 4 cross times 1 cross times 16 end root over denominator 2 cross times 1 end fraction space space space space o r space space x squared plus 6 x minus x minus 6 equals 0 x equals fraction numerator negative 5 plus-or-minus square root of negative 39 end root over denominator 2 end fraction left parenthesis r e j e c t right parenthesis space space space space space space space space space space space o r space space x left parenthesis x plus 6 right parenthesis minus 1 left parenthesis x plus 6 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space o r space space left parenthesis x plus 6 right parenthesis left parenthesis x minus 1 right parenthesis equals 0 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space o r space space space x equals negative 6 space space space a n d space x equals 1$

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