Question

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

Answer 1

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`