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Simplifying 3p2 + -6p = 1 Reorder the terms: -6p + 3p2 = 1 Solving -6p + 3p2 = 1 Solving for variable 'p'. Reorder the terms: -1 + -6p + 3p2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -6p + 3p2 = 0 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 = 2.154700538 p = 2.154700538 Simplifying p = 2.154700538Subproblem 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 = -0.154700538 p = -0.154700538 Simplifying p = -0.154700538Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.154700538, -0.154700538}
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