How do you solve #36p ^ { 2} - 72p - 45= 0#?

1 Answer
Nghi N
May 12, 2017

#-1/2 and 5/2#

Explanation:

First simplify by 9 and solve the quadratic equation:
#f(p) = 4p^2 - 8p - 5 = 0#
Use the new Transforming Method (Socratic Search)
Transformed equation:
#f'(p) = p^2 - 8p - 20 = 0#
Method: find 2 real roots of f'(p), then divide them by a = 4.
Find 2 real roots of f'(p), knowing sum (-b = 8) and product (c = -20).
They are of the factor pair (-2, 10).
The 2 real root of original f() are:
#p1 = -2/a = -2/4 = - 1/2#
#p2 = 10/a = 10/4 = 5/2#

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