Solve the equation 8p2−46p+63=0.

This is a quadratic equation in the form of ax^2 + bx + c = 0. The general solution for such equations is given by the quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Here, a = 8, b = -46, and c = 63.

Step 1: Calculate the discriminant, which is b^2 - 4ac. Discriminant = (-46)^2 - 4863 = 2116 - 2016 = 100.

Step 2: Substitute a, b, and the discriminant into the quadratic formula to find the solutions.

p = [46 ± sqrt(100)] / (2*8) = [46 ± 10] / 16

So, the solutions are:

p1 = (46 + 10) / 16 = 56 / 16 = 3.5 p2 = (46 - 10) / 16 = 36 / 16 = 2.25

So, the solutions to the equation 8p^2 - 46p + 63 = 0 are p = 3.5 and p = 2.25.