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Simplifying p = 54p2 + -5 Reorder the terms: p = -5 + 54p2 Solving p = -5 + 54p2 Solving for variable 'p'. Reorder the terms: 5 + p + -54p2 = -5 + 54p2 + 5 + -54p2 Reorder the terms: 5 + p + -54p2 = -5 + 5 + 54p2 + -54p2 Combine like terms: -5 + 5 = 0 5 + p + -54p2 = 0 + 54p2 + -54p2 5 + p + -54p2 = 54p2 + -54p2 Combine like terms: 54p2 + -54p2 = 0 5 + p + -54p2 = 0 Begin completing the square. Divide all terms by -54 the coefficient of the squared term: Divide each side by '-54'. -0.09259259259 + -0.01851851852p + p2 = 0 Move the constant term to the right: Add '0.09259259259' to each side of the equation. -0.09259259259 + -0.01851851852p + 0.09259259259 + p2 = 0 + 0.09259259259 Reorder the terms: -0.09259259259 + 0.09259259259 + -0.01851851852p + p2 = 0 + 0.09259259259 Combine like terms: -0.09259259259 + 0.09259259259 = 0.00000000000 0.00000000000 + -0.01851851852p + p2 = 0 + 0.09259259259 -0.01851851852p + p2 = 0 + 0.09259259259 Combine like terms: 0 + 0.09259259259 = 0.09259259259 -0.01851851852p + p2 = 0.09259259259 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. -0.01851851852p + 0.25 + p2 = 0.09259259259 + 0.25 Reorder the terms: 0.25 + -0.01851851852p + p2 = 0.09259259259 + 0.25 Combine like terms: 0.09259259259 + 0.25 = 0.34259259259 0.25 + -0.01851851852p + p2 = 0.34259259259 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 0.34259259259 Calculate the square root of the right side: 0.585314097 Break this problem into two subproblems by setting (p + 0.5) equal to 0.585314097 and -0.585314097.Subproblem 1
p + 0.5 = 0.585314097 Simplifying p + 0.5 = 0.585314097 Reorder the terms: 0.5 + p = 0.585314097 Solving 0.5 + p = 0.585314097 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 = 0.585314097 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 0.585314097 + -0.5 p = 0.585314097 + -0.5 Combine like terms: 0.585314097 + -0.5 = 0.085314097 p = 0.085314097 Simplifying p = 0.085314097Subproblem 2
p + 0.5 = -0.585314097 Simplifying p + 0.5 = -0.585314097 Reorder the terms: 0.5 + p = -0.585314097 Solving 0.5 + p = -0.585314097 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 = -0.585314097 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -0.585314097 + -0.5 p = -0.585314097 + -0.5 Combine like terms: -0.585314097 + -0.5 = -1.085314097 p = -1.085314097 Simplifying p = -1.085314097Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.085314097, -1.085314097}
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