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Question

Solve the following quadratic equation by factorization.
1x+41x7=1130,x4,7

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Solution

fraction numerator 1 over denominator x plus 4 end fraction minus fraction numerator 1 over denominator x minus 7 end fraction equals 11 over 30 fraction numerator x minus 7 minus x minus 4 over denominator left parenthesis x plus 4 right parenthesis left parenthesis x minus 7 right parenthesis end fraction equals 11 over 30 fraction numerator negative up diagonal strike 11 over denominator left parenthesis x plus 4 right parenthesis left parenthesis x minus 7 right parenthesis end fraction equals fraction numerator up diagonal strike 11 over denominator 30 end fraction left parenthesis x plus 4 right parenthesis left parenthesis x minus 7 right parenthesis equals negative 30 x squared minus 3 x minus 28 plus 30 equals 0 x squared minus 3 x plus 2 equals 0
product of 1 and 2 = 2
which can be written as -2 x -1
-2 -1= -3

x squared minus 2 x minus x plus 2 equals 0 x left parenthesis x minus 2 right parenthesis minus 1 left parenthesis x minus 2 right parenthesis equals 0 left parenthesis x minus 1 right parenthesis left parenthesis x minus 2 right parenthesis equals 0 x equals 1 comma 2

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