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Simplifying -3p2 = -6p + -7 Reorder the terms: -3p2 = -7 + -6p Solving -3p2 = -7 + -6p Solving for variable 'p'. Reorder the terms: 7 + 6p + -3p2 = -7 + -6p + 7 + 6p Reorder the terms: 7 + 6p + -3p2 = -7 + 7 + -6p + 6p Combine like terms: -7 + 7 = 0 7 + 6p + -3p2 = 0 + -6p + 6p 7 + 6p + -3p2 = -6p + 6p Combine like terms: -6p + 6p = 0 7 + 6p + -3p2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -2.333333333 + -2p + p2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -2p + 2.333333333 + p2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -2p + p2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -2p + p2 = 0 + 2.333333333 -2p + p2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -2p + p2 = 2.333333333 The p term is -2p. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2p + 1 + p2 = 2.333333333 + 1 Reorder the terms: 1 + -2p + p2 = 2.333333333 + 1 Combine like terms: 2.333333333 + 1 = 3.333333333 1 + -2p + p2 = 3.333333333 Factor a perfect square on the left side: (p + -1)(p + -1) = 3.333333333 Calculate the square root of the right side: 1.825741858 Break this problem into two subproblems by setting (p + -1) equal to 1.825741858 and -1.825741858.Subproblem 1
p + -1 = 1.825741858 Simplifying p + -1 = 1.825741858 Reorder the terms: -1 + p = 1.825741858 Solving -1 + p = 1.825741858 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = 1.825741858 + 1 Combine like terms: -1 + 1 = 0 0 + p = 1.825741858 + 1 p = 1.825741858 + 1 Combine like terms: 1.825741858 + 1 = 2.825741858 p = 2.825741858 Simplifying p = 2.825741858Subproblem 2
p + -1 = -1.825741858 Simplifying p + -1 = -1.825741858 Reorder the terms: -1 + p = -1.825741858 Solving -1 + p = -1.825741858 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = -1.825741858 + 1 Combine like terms: -1 + 1 = 0 0 + p = -1.825741858 + 1 p = -1.825741858 + 1 Combine like terms: -1.825741858 + 1 = -0.825741858 p = -0.825741858 Simplifying p = -0.825741858Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.825741858, -0.825741858}
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