p^2=44-p

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Solution for p^2=44-p equation:


Simplifying
p2 = 44 + -1p

Solving
p2 = 44 + -1p

Solving for variable 'p'.

Reorder the terms:
-44 + p + p2 = 44 + -1p + -44 + p

Reorder the terms:
-44 + p + p2 = 44 + -44 + -1p + p

Combine like terms: 44 + -44 = 0
-44 + p + p2 = 0 + -1p + p
-44 + p + p2 = -1p + p

Combine like terms: -1p + p = 0
-44 + p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + p + 44 + p2 = 0 + 44

Reorder the terms:
-44 + 44 + p + p2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + p + p2 = 0 + 44
p + p2 = 0 + 44

Combine like terms: 0 + 44 = 44
p + p2 = 44

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 = 44 + 0.25

Reorder the terms:
0.25 + p + p2 = 44 + 0.25

Combine like terms: 44 + 0.25 = 44.25
0.25 + p + p2 = 44.25

Factor a perfect square on the left side:
(p + 0.5)(p + 0.5) = 44.25

Calculate the square root of the right side: 6.652067348

Break this problem into two subproblems by setting 
(p + 0.5) equal to 6.652067348 and -6.652067348.

Subproblem 1

p + 0.5 = 6.652067348 Simplifying p + 0.5 = 6.652067348 Reorder the terms: 0.5 + p = 6.652067348 Solving 0.5 + p = 6.652067348 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 = 6.652067348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 6.652067348 + -0.5 p = 6.652067348 + -0.5 Combine like terms: 6.652067348 + -0.5 = 6.152067348 p = 6.152067348 Simplifying p = 6.152067348

Subproblem 2

p + 0.5 = -6.652067348 Simplifying p + 0.5 = -6.652067348 Reorder the terms: 0.5 + p = -6.652067348 Solving 0.5 + p = -6.652067348 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 = -6.652067348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -6.652067348 + -0.5 p = -6.652067348 + -0.5 Combine like terms: -6.652067348 + -0.5 = -7.152067348 p = -7.152067348 Simplifying p = -7.152067348

Solution

The solution to the problem is based on the solutions from the subproblems. p = {6.152067348, -7.152067348}

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