P^2-P=0.24

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Solution for P^2-P=0.24 equation: 


Simplifying
P2 + -1P = 0.24

Reorder the terms:
-1P + P2 = 0.24

Solving
-1P + P2 = 0.24

Solving for variable 'P'.

Reorder the terms:
-0.24 + -1P + P2 = 0.24 + -0.24

Combine like terms: 0.24 + -0.24 = 0.00
-0.24 + -1P + P2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.24' to each side of the equation.
-0.24 + -1P + 0.24 + P2 = 0.00 + 0.24

Reorder the terms:
-0.24 + 0.24 + -1P + P2 = 0.00 + 0.24

Combine like terms: -0.24 + 0.24 = 0.00
0.00 + -1P + P2 = 0.00 + 0.24
-1P + P2 = 0.00 + 0.24

Combine like terms: 0.00 + 0.24 = 0.24
-1P + P2 = 0.24

The P term is -1P.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1P + 0.25 + P2 = 0.24 + 0.25

Reorder the terms:
0.25 + -1P + P2 = 0.24 + 0.25

Combine like terms: 0.24 + 0.25 = 0.49
0.25 + -1P + P2 = 0.49

Factor a perfect square on the left side:
(P + -0.5)(P + -0.5) = 0.49

Calculate the square root of the right side: 0.7

Break this problem into two subproblems by setting 
(P + -0.5) equal to 0.7 and -0.7.


Subproblem 1
P + -0.5 = 0.7

Simplifying
P + -0.5 = 0.7

Reorder the terms:
-0.5 + P = 0.7

Solving
-0.5 + P = 0.7

Solving for variable 'P'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + P = 0.7 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + P = 0.7 + 0.5
P = 0.7 + 0.5

Combine like terms: 0.7 + 0.5 = 1.2
P = 1.2

Simplifying
P = 1.2


Subproblem 2
P + -0.5 = -0.7

Simplifying
P + -0.5 = -0.7

Reorder the terms:
-0.5 + P = -0.7

Solving
-0.5 + P = -0.7

Solving for variable 'P'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + P = -0.7 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + P = -0.7 + 0.5
P = -0.7 + 0.5

Combine like terms: -0.7 + 0.5 = -0.2
P = -0.2

Simplifying
P = -0.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
P = {1.2, -0.2}

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