solving but not getting the answer

x2 − 21.75x = −15.75
Is this supposed to be
x2 − 21.75x = −15.75
If so, rearrange to
x2 − 21.75x +15.75 = 0
and use the quadratic formula (eyeballing looks like about 2.5 and 19)
 
Is this supposed to be
x2 − 21.75x = −15.75
If so, rearrange to
x2 − 21.75x +15.75 = 0
and use the quadratic formula (eyeballing looks like about 2.5 and 19)

cant use formula
has to be solved fairly quickly
did the box method but takes too long
 
cant use formula
has to be solved fairly quickly
did the box method but takes too long
Can you try an iterative method
\(\displaystyle x_{i+1} = x_i - \dfrac{x_i^2 − 21.75 x_i + 15.75}{2 x_i − 21.75}\)
For the two different roots start with my two guess above although they are not all that good. It shouldn't take more than 3 or 4 iterates.
 
Multiply by 4:
4x^2 - 87x + 63 = 0
Factor:
(4x - 3)(? - ?) = 0
Finish it...

(4x - 3) is only one of many potential factors to consider for the first factor. Others are:

(4x - 1), (4x - 7), (4x - 9), (4x - 21), (4x - 63), (2x - 1), (2x - 3), etc.
 
(4x - 3) is only one of many potential factors to consider for the first factor. Others are:

(4x - 1), (4x - 7), (4x - 9), (4x - 21), (4x - 63), (2x - 1), (2x - 3), etc.
Not if you know the answer
 
Not if you know the answer

The student can't read Denis's mind. Denis revealed no reason as to why he chose that
factor for the student (if it does work).

And if it's a case of the tutor thinking/working "I happen to know this partial combination
of factors that works," then that part isn't a help to the student.
 
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