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Simplifying 3p2 + -6p + -19 = 0 Reorder the terms: -19 + -6p + 3p2 = 0 Solving -19 + -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'. -6.333333333 + -2p + p2 = 0 Move the constant term to the right: Add '6.333333333' to each side of the equation. -6.333333333 + -2p + 6.333333333 + p2 = 0 + 6.333333333 Reorder the terms: -6.333333333 + 6.333333333 + -2p + p2 = 0 + 6.333333333 Combine like terms: -6.333333333 + 6.333333333 = 0.000000000 0.000000000 + -2p + p2 = 0 + 6.333333333 -2p + p2 = 0 + 6.333333333 Combine like terms: 0 + 6.333333333 = 6.333333333 -2p + p2 = 6.333333333 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 = 6.333333333 + 1 Reorder the terms: 1 + -2p + p2 = 6.333333333 + 1 Combine like terms: 6.333333333 + 1 = 7.333333333 1 + -2p + p2 = 7.333333333 Factor a perfect square on the left side: (p + -1)(p + -1) = 7.333333333 Calculate the square root of the right side: 2.708012801 Break this problem into two subproblems by setting (p + -1) equal to 2.708012801 and -2.708012801.Subproblem 1
p + -1 = 2.708012801 Simplifying p + -1 = 2.708012801 Reorder the terms: -1 + p = 2.708012801 Solving -1 + p = 2.708012801 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 = 2.708012801 + 1 Combine like terms: -1 + 1 = 0 0 + p = 2.708012801 + 1 p = 2.708012801 + 1 Combine like terms: 2.708012801 + 1 = 3.708012801 p = 3.708012801 Simplifying p = 3.708012801Subproblem 2
p + -1 = -2.708012801 Simplifying p + -1 = -2.708012801 Reorder the terms: -1 + p = -2.708012801 Solving -1 + p = -2.708012801 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 = -2.708012801 + 1 Combine like terms: -1 + 1 = 0 0 + p = -2.708012801 + 1 p = -2.708012801 + 1 Combine like terms: -2.708012801 + 1 = -1.708012801 p = -1.708012801 Simplifying p = -1.708012801Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.708012801, -1.708012801}
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