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Simplifying -2p2 + -10p + 3 = 0 Reorder the terms: 3 + -10p + -2p2 = 0 Solving 3 + -10p + -2p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1.5 + 5p + p2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 5p + 1.5 + p2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 5p + p2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 5p + p2 = 0 + 1.5 5p + p2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 5p + p2 = 1.5 The p term is 5p. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5p + 6.25 + p2 = 1.5 + 6.25 Reorder the terms: 6.25 + 5p + p2 = 1.5 + 6.25 Combine like terms: 1.5 + 6.25 = 7.75 6.25 + 5p + p2 = 7.75 Factor a perfect square on the left side: (p + 2.5)(p + 2.5) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (p + 2.5) equal to 2.783882181 and -2.783882181.Subproblem 1
p + 2.5 = 2.783882181 Simplifying p + 2.5 = 2.783882181 Reorder the terms: 2.5 + p = 2.783882181 Solving 2.5 + p = 2.783882181 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = 2.783882181 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = 2.783882181 + -2.5 p = 2.783882181 + -2.5 Combine like terms: 2.783882181 + -2.5 = 0.283882181 p = 0.283882181 Simplifying p = 0.283882181Subproblem 2
p + 2.5 = -2.783882181 Simplifying p + 2.5 = -2.783882181 Reorder the terms: 2.5 + p = -2.783882181 Solving 2.5 + p = -2.783882181 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + p = -2.783882181 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + p = -2.783882181 + -2.5 p = -2.783882181 + -2.5 Combine like terms: -2.783882181 + -2.5 = -5.283882181 p = -5.283882181 Simplifying p = -5.283882181Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.283882181, -5.283882181}
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