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Simplifying 3p(2p + -1) = 3.3219 Reorder the terms: 3p(-1 + 2p) = 3.3219 (-1 * 3p + 2p * 3p) = 3.3219 (-3p + 6p2) = 3.3219 Solving -3p + 6p2 = 3.3219 Solving for variable 'p'. Reorder the terms: -3.3219 + -3p + 6p2 = 3.3219 + -3.3219 Combine like terms: 3.3219 + -3.3219 = 0.0000 -3.3219 + -3p + 6p2 = 0.0000 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.55365 + -0.5p + p2 = 0.0000 Move the constant term to the right: Add '0.55365' to each side of the equation. -0.55365 + -0.5p + 0.55365 + p2 = 0.0000 + 0.55365 Reorder the terms: -0.55365 + 0.55365 + -0.5p + p2 = 0.0000 + 0.55365 Combine like terms: -0.55365 + 0.55365 = 0.00000 0.00000 + -0.5p + p2 = 0.0000 + 0.55365 -0.5p + p2 = 0.0000 + 0.55365 Combine like terms: 0.0000 + 0.55365 = 0.55365 -0.5p + p2 = 0.55365 The p term is -0.5p. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5p + 0.0625 + p2 = 0.55365 + 0.0625 Reorder the terms: 0.0625 + -0.5p + p2 = 0.55365 + 0.0625 Combine like terms: 0.55365 + 0.0625 = 0.61615 0.0625 + -0.5p + p2 = 0.61615 Factor a perfect square on the left side: (p + -0.25)(p + -0.25) = 0.61615 Calculate the square root of the right side: 0.784952228 Break this problem into two subproblems by setting (p + -0.25) equal to 0.784952228 and -0.784952228.Subproblem 1
p + -0.25 = 0.784952228 Simplifying p + -0.25 = 0.784952228 Reorder the terms: -0.25 + p = 0.784952228 Solving -0.25 + p = 0.784952228 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + p = 0.784952228 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + p = 0.784952228 + 0.25 p = 0.784952228 + 0.25 Combine like terms: 0.784952228 + 0.25 = 1.034952228 p = 1.034952228 Simplifying p = 1.034952228Subproblem 2
p + -0.25 = -0.784952228 Simplifying p + -0.25 = -0.784952228 Reorder the terms: -0.25 + p = -0.784952228 Solving -0.25 + p = -0.784952228 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + p = -0.784952228 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + p = -0.784952228 + 0.25 p = -0.784952228 + 0.25 Combine like terms: -0.784952228 + 0.25 = -0.534952228 p = -0.534952228 Simplifying p = -0.534952228Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.034952228, -0.534952228}
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