p^2-1.2p=0.45

Solution for p^2-1.2p=0.45 equation:

Simplifying
p2 + -1.2p = 0.45

Reorder the terms:
-1.2p + p2 = 0.45

Solving
-1.2p + p2 = 0.45

Solving for variable 'p'.

Reorder the terms:
-0.45 + -1.2p + p2 = 0.45 + -0.45

Combine like terms: 0.45 + -0.45 = 0.00
-0.45 + -1.2p + p2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.45' to each side of the equation.
-0.45 + -1.2p + 0.45 + p2 = 0.00 + 0.45

Reorder the terms:
-0.45 + 0.45 + -1.2p + p2 = 0.00 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + -1.2p + p2 = 0.00 + 0.45
-1.2p + p2 = 0.00 + 0.45

Combine like terms: 0.00 + 0.45 = 0.45
-1.2p + p2 = 0.45

The p term is -1.2p.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2p + 0.36 + p2 = 0.45 + 0.36

Reorder the terms:
0.36 + -1.2p + p2 = 0.45 + 0.36

Combine like terms: 0.45 + 0.36 = 0.81
0.36 + -1.2p + p2 = 0.81

Factor a perfect square on the left side:
(p + -0.6)(p + -0.6) = 0.81

Calculate the square root of the right side: 0.9

Break this problem into two subproblems by setting 
(p + -0.6) equal to 0.9 and -0.9.

Subproblem 1
p + -0.6 = 0.9

Simplifying
p + -0.6 = 0.9

Reorder the terms:
-0.6 + p = 0.9

Solving
-0.6 + p = 0.9

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '0.6' to each side of the equation.
-0.6 + 0.6 + p = 0.9 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + p = 0.9 + 0.6
p = 0.9 + 0.6

Combine like terms: 0.9 + 0.6 = 1.5
p = 1.5

Simplifying
p = 1.5

Subproblem 2
p + -0.6 = -0.9

Simplifying
p + -0.6 = -0.9

Reorder the terms:
-0.6 + p = -0.9

Solving
-0.6 + p = -0.9

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '0.6' to each side of the equation.
-0.6 + 0.6 + p = -0.9 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + p = -0.9 + 0.6
p = -0.9 + 0.6

Combine like terms: -0.9 + 0.6 = -0.3
p = -0.3

Simplifying
p = -0.3

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.5, -0.3}