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Question
Solve the following quadratic equation by factorization:
`(x-5)(x-6)=25/(24)^2`
Solution
We have been given that,
`(x-5)(x-6)=25/(24)^2`
`(x-5)(x-6)=25/576`
`x^2-11x+30-25/576=0`
`x^2-11x+17255/576=0`
`x^2-145/24x-119/24x+17255/576=0`
`x(x-145/24)-119/24(x-145/24)=0`
`(x-119/24)(x-145/24)=0`
Therefore,
`x-119/24=0`
`x=119/24`
or,
`x-145/24=0`
`x=145/24`
Hence, `x = 119/24 = 4 23/24` or `x = 145/24 = 6 1/24`
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