# How do you solve #23p = 5p² + 24#?

##### 2 Answers

#### Explanation:

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.

#### Explanation:

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: