How do you solve #20t ^ { 2} - 17t = 63#?

1 Answer
bp
Dec 9, 2016

t= #-7/5 or 9/4#

Explanation:

This can be solved by either using quadratic formula or by factorising the quadratic #20t^2 -17t-63=0# by splitting the middle term. The latter would be quite simpler. Consider the product of the coefficient of #t^2# and the constant term that is 20(-63). Now split this in two parts so that their sum or difference is -17. Now, factorise 20(-63)= 45(-9)7= 28(-45). The sum of 28and -45 gives -17. Thus write the quadratic as #20t^2 -45t +28t -63=0# . Now pair the terms as follows

#(20t^2 -45t) +(28t-63)=0

#5t(4t-9) +7(4t-9)=0#
(5t+7)(4t-9)=0
7
This gives t= #-7/5# or t=#9/4#

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