How do you solve #23p = 5p² + 24#?
Solve quadratic equations by making them equal to 0.
Factorise: Find factors of 5 and 8 which add to give 23. Signs will be the same they are both negative.
Cross multiply the factors:
Either of the factors could be equal to 0.
Solve this quadratic equation by the new Transforming Method (Socratic Search).
Method. First find the 2 real roots of the transformed equation,
y' = p^2 - 23p + 120 = 0. Next, divide the answers by (a) to get the
2 real roots of y.
Two real roots of y' have same sign (Rule of signs)
Factor pairs of (ac = 120) --> (4, 30)(5, 24)(8, 15). This last sum is
23 = -b. The 2 real roots of y' are: 8 and 15.
Back to original equation y, the 2 real roots are: