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Simplifying 9p2 + p + -8091 = 0 Reorder the terms: -8091 + p + 9p2 = 0 Solving -8091 + p + 9p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -899 + 0.1111111111p + p2 = 0 Move the constant term to the right: Add '899' to each side of the equation. -899 + 0.1111111111p + 899 + p2 = 0 + 899 Reorder the terms: -899 + 899 + 0.1111111111p + p2 = 0 + 899 Combine like terms: -899 + 899 = 0 0 + 0.1111111111p + p2 = 0 + 899 0.1111111111p + p2 = 0 + 899 Combine like terms: 0 + 899 = 899 0.1111111111p + p2 = 899 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. 0.1111111111p + 0.25 + p2 = 899 + 0.25 Reorder the terms: 0.25 + 0.1111111111p + p2 = 899 + 0.25 Combine like terms: 899 + 0.25 = 899.25 0.25 + 0.1111111111p + p2 = 899.25 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 899.25 Calculate the square root of the right side: 29.987497395 Break this problem into two subproblems by setting (p + 0.5) equal to 29.987497395 and -29.987497395.Subproblem 1
p + 0.5 = 29.987497395 Simplifying p + 0.5 = 29.987497395 Reorder the terms: 0.5 + p = 29.987497395 Solving 0.5 + p = 29.987497395 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 = 29.987497395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 29.987497395 + -0.5 p = 29.987497395 + -0.5 Combine like terms: 29.987497395 + -0.5 = 29.487497395 p = 29.487497395 Simplifying p = 29.487497395Subproblem 2
p + 0.5 = -29.987497395 Simplifying p + 0.5 = -29.987497395 Reorder the terms: 0.5 + p = -29.987497395 Solving 0.5 + p = -29.987497395 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 = -29.987497395 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -29.987497395 + -0.5 p = -29.987497395 + -0.5 Combine like terms: -29.987497395 + -0.5 = -30.487497395 p = -30.487497395 Simplifying p = -30.487497395Solution
The solution to the problem is based on the solutions from the subproblems. p = {29.487497395, -30.487497395}
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