p=27-p^2

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Solution for p=27-p^2 equation:


Simplifying
p = 27 + -1p2

Solving
p = 27 + -1p2

Solving for variable 'p'.

Reorder the terms:
-27 + p + p2 = 27 + -1p2 + -27 + p2

Reorder the terms:
-27 + p + p2 = 27 + -27 + -1p2 + p2

Combine like terms: 27 + -27 = 0
-27 + p + p2 = 0 + -1p2 + p2
-27 + p + p2 = -1p2 + p2

Combine like terms: -1p2 + p2 = 0
-27 + p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + p + 27 + p2 = 0 + 27

Reorder the terms:
-27 + 27 + p + p2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + p + p2 = 0 + 27
p + p2 = 0 + 27

Combine like terms: 0 + 27 = 27
p + p2 = 27

The p term is p.  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.
p + 0.25 + p2 = 27 + 0.25

Reorder the terms:
0.25 + p + p2 = 27 + 0.25

Combine like terms: 27 + 0.25 = 27.25
0.25 + p + p2 = 27.25

Factor a perfect square on the left side:
(p + 0.5)(p + 0.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(p + 0.5) equal to 5.220153254 and -5.220153254.

Subproblem 1

p + 0.5 = 5.220153254 Simplifying p + 0.5 = 5.220153254 Reorder the terms: 0.5 + p = 5.220153254 Solving 0.5 + p = 5.220153254 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 = 5.220153254 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 5.220153254 + -0.5 p = 5.220153254 + -0.5 Combine like terms: 5.220153254 + -0.5 = 4.720153254 p = 4.720153254 Simplifying p = 4.720153254

Subproblem 2

p + 0.5 = -5.220153254 Simplifying p + 0.5 = -5.220153254 Reorder the terms: 0.5 + p = -5.220153254 Solving 0.5 + p = -5.220153254 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 = -5.220153254 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -5.220153254 + -0.5 p = -5.220153254 + -0.5 Combine like terms: -5.220153254 + -0.5 = -5.720153254 p = -5.720153254 Simplifying p = -5.720153254

Solution

The solution to the problem is based on the solutions from the subproblems. p = {4.720153254, -5.720153254}

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