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Simplifying 2000 = -4p2 + 60p + 1039 Reorder the terms: 2000 = 1039 + 60p + -4p2 Solving 2000 = 1039 + 60p + -4p2 Solving for variable 'p'. Combine like terms: 2000 + -1039 = 961 961 + -60p + 4p2 = 1039 + 60p + -4p2 + -1039 + -60p + 4p2 Reorder the terms: 961 + -60p + 4p2 = 1039 + -1039 + 60p + -60p + -4p2 + 4p2 Combine like terms: 1039 + -1039 = 0 961 + -60p + 4p2 = 0 + 60p + -60p + -4p2 + 4p2 961 + -60p + 4p2 = 60p + -60p + -4p2 + 4p2 Combine like terms: 60p + -60p = 0 961 + -60p + 4p2 = 0 + -4p2 + 4p2 961 + -60p + 4p2 = -4p2 + 4p2 Combine like terms: -4p2 + 4p2 = 0 961 + -60p + 4p2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 240.25 + -15p + p2 = 0 Move the constant term to the right: Add '-240.25' to each side of the equation. 240.25 + -15p + -240.25 + p2 = 0 + -240.25 Reorder the terms: 240.25 + -240.25 + -15p + p2 = 0 + -240.25 Combine like terms: 240.25 + -240.25 = 0.00 0.00 + -15p + p2 = 0 + -240.25 -15p + p2 = 0 + -240.25 Combine like terms: 0 + -240.25 = -240.25 -15p + p2 = -240.25 The p term is -15p. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15p + 56.25 + p2 = -240.25 + 56.25 Reorder the terms: 56.25 + -15p + p2 = -240.25 + 56.25 Combine like terms: -240.25 + 56.25 = -184 56.25 + -15p + p2 = -184 Factor a perfect square on the left side: (p + -7.5)(p + -7.5) = -184 Can't calculate square root of the right side. The solution to this equation could not be determined.
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