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Simplifying p2 + -26p + 133 = p Reorder the terms: 133 + -26p + p2 = p Solving 133 + -26p + p2 = p Solving for variable 'p'. Reorder the terms: 133 + -26p + -1p + p2 = p + -1p Combine like terms: -26p + -1p = -27p 133 + -27p + p2 = p + -1p Combine like terms: p + -1p = 0 133 + -27p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '-133' to each side of the equation. 133 + -27p + -133 + p2 = 0 + -133 Reorder the terms: 133 + -133 + -27p + p2 = 0 + -133 Combine like terms: 133 + -133 = 0 0 + -27p + p2 = 0 + -133 -27p + p2 = 0 + -133 Combine like terms: 0 + -133 = -133 -27p + p2 = -133 The p term is -27p. Take half its coefficient (-13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. -27p + 182.25 + p2 = -133 + 182.25 Reorder the terms: 182.25 + -27p + p2 = -133 + 182.25 Combine like terms: -133 + 182.25 = 49.25 182.25 + -27p + p2 = 49.25 Factor a perfect square on the left side: (p + -13.5)(p + -13.5) = 49.25 Calculate the square root of the right side: 7.017834424 Break this problem into two subproblems by setting (p + -13.5) equal to 7.017834424 and -7.017834424.Subproblem 1
p + -13.5 = 7.017834424 Simplifying p + -13.5 = 7.017834424 Reorder the terms: -13.5 + p = 7.017834424 Solving -13.5 + p = 7.017834424 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + p = 7.017834424 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + p = 7.017834424 + 13.5 p = 7.017834424 + 13.5 Combine like terms: 7.017834424 + 13.5 = 20.517834424 p = 20.517834424 Simplifying p = 20.517834424Subproblem 2
p + -13.5 = -7.017834424 Simplifying p + -13.5 = -7.017834424 Reorder the terms: -13.5 + p = -7.017834424 Solving -13.5 + p = -7.017834424 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '13.5' to each side of the equation. -13.5 + 13.5 + p = -7.017834424 + 13.5 Combine like terms: -13.5 + 13.5 = 0.0 0.0 + p = -7.017834424 + 13.5 p = -7.017834424 + 13.5 Combine like terms: -7.017834424 + 13.5 = 6.482165576 p = 6.482165576 Simplifying p = 6.482165576Solution
The solution to the problem is based on the solutions from the subproblems. p = {20.517834424, 6.482165576}
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