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Simplifying 3p2 + 6p + -1 = 0 Reorder the terms: -1 + 6p + 3p2 = 0 Solving -1 + 6p + 3p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + 2p + p2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 2p + 0.3333333333 + p2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 2p + p2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 2p + p2 = 0 + 0.3333333333 2p + p2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 2p + p2 = 0.3333333333 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 = 0.3333333333 + 1 Reorder the terms: 1 + 2p + p2 = 0.3333333333 + 1 Combine like terms: 0.3333333333 + 1 = 1.3333333333 1 + 2p + p2 = 1.3333333333 Factor a perfect square on the left side: (p + 1)(p + 1) = 1.3333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (p + 1) equal to 1.154700538 and -1.154700538.Subproblem 1
p + 1 = 1.154700538 Simplifying p + 1 = 1.154700538 Reorder the terms: 1 + p = 1.154700538 Solving 1 + p = 1.154700538 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 = 1.154700538 + -1 Combine like terms: 1 + -1 = 0 0 + p = 1.154700538 + -1 p = 1.154700538 + -1 Combine like terms: 1.154700538 + -1 = 0.154700538 p = 0.154700538 Simplifying p = 0.154700538Subproblem 2
p + 1 = -1.154700538 Simplifying p + 1 = -1.154700538 Reorder the terms: 1 + p = -1.154700538 Solving 1 + p = -1.154700538 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 = -1.154700538 + -1 Combine like terms: 1 + -1 = 0 0 + p = -1.154700538 + -1 p = -1.154700538 + -1 Combine like terms: -1.154700538 + -1 = -2.154700538 p = -2.154700538 Simplifying p = -2.154700538Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.154700538, -2.154700538}
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