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Simplifying 3p2 + -436p + 11236 = 0 Reorder the terms: 11236 + -436p + 3p2 = 0 Solving 11236 + -436p + 3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3745.333333 + -145.3333333p + p2 = 0 Move the constant term to the right: Add '-3745.333333' to each side of the equation. 3745.333333 + -145.3333333p + -3745.333333 + p2 = 0 + -3745.333333 Reorder the terms: 3745.333333 + -3745.333333 + -145.3333333p + p2 = 0 + -3745.333333 Combine like terms: 3745.333333 + -3745.333333 = 0.000000 0.000000 + -145.3333333p + p2 = 0 + -3745.333333 -145.3333333p + p2 = 0 + -3745.333333 Combine like terms: 0 + -3745.333333 = -3745.333333 -145.3333333p + p2 = -3745.333333 The p term is -145.3333333p. Take half its coefficient (-72.66666665). Square it (5280.444442) and add it to both sides. Add '5280.444442' to each side of the equation. -145.3333333p + 5280.444442 + p2 = -3745.333333 + 5280.444442 Reorder the terms: 5280.444442 + -145.3333333p + p2 = -3745.333333 + 5280.444442 Combine like terms: -3745.333333 + 5280.444442 = 1535.111109 5280.444442 + -145.3333333p + p2 = 1535.111109 Factor a perfect square on the left side: (p + -72.66666665)(p + -72.66666665) = 1535.111109 Calculate the square root of the right side: 39.180493986 Break this problem into two subproblems by setting (p + -72.66666665) equal to 39.180493986 and -39.180493986.Subproblem 1
p + -72.66666665 = 39.180493986 Simplifying p + -72.66666665 = 39.180493986 Reorder the terms: -72.66666665 + p = 39.180493986 Solving -72.66666665 + p = 39.180493986 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '72.66666665' to each side of the equation. -72.66666665 + 72.66666665 + p = 39.180493986 + 72.66666665 Combine like terms: -72.66666665 + 72.66666665 = 0.00000000 0.00000000 + p = 39.180493986 + 72.66666665 p = 39.180493986 + 72.66666665 Combine like terms: 39.180493986 + 72.66666665 = 111.847160636 p = 111.847160636 Simplifying p = 111.847160636Subproblem 2
p + -72.66666665 = -39.180493986 Simplifying p + -72.66666665 = -39.180493986 Reorder the terms: -72.66666665 + p = -39.180493986 Solving -72.66666665 + p = -39.180493986 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '72.66666665' to each side of the equation. -72.66666665 + 72.66666665 + p = -39.180493986 + 72.66666665 Combine like terms: -72.66666665 + 72.66666665 = 0.00000000 0.00000000 + p = -39.180493986 + 72.66666665 p = -39.180493986 + 72.66666665 Combine like terms: -39.180493986 + 72.66666665 = 33.486172664 p = 33.486172664 Simplifying p = 33.486172664Solution
The solution to the problem is based on the solutions from the subproblems. p = {111.847160636, 33.486172664}
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