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Simplifying 3p2 + -3p + -5 = 0 Reorder the terms: -5 + -3p + 3p2 = 0 Solving -5 + -3p + 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'. -1.666666667 + -1p + p2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -1p + 1.666666667 + p2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -1p + p2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -1p + p2 = 0 + 1.666666667 -1p + p2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -1p + p2 = 1.666666667 The p term is -1p. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1p + 0.25 + p2 = 1.666666667 + 0.25 Reorder the terms: 0.25 + -1p + p2 = 1.666666667 + 0.25 Combine like terms: 1.666666667 + 0.25 = 1.916666667 0.25 + -1p + p2 = 1.916666667 Factor a perfect square on the left side: (p + -0.5)(p + -0.5) = 1.916666667 Calculate the square root of the right side: 1.384437311 Break this problem into two subproblems by setting (p + -0.5) equal to 1.384437311 and -1.384437311.Subproblem 1
p + -0.5 = 1.384437311 Simplifying p + -0.5 = 1.384437311 Reorder the terms: -0.5 + p = 1.384437311 Solving -0.5 + p = 1.384437311 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = 1.384437311 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = 1.384437311 + 0.5 p = 1.384437311 + 0.5 Combine like terms: 1.384437311 + 0.5 = 1.884437311 p = 1.884437311 Simplifying p = 1.884437311Subproblem 2
p + -0.5 = -1.384437311 Simplifying p + -0.5 = -1.384437311 Reorder the terms: -0.5 + p = -1.384437311 Solving -0.5 + p = -1.384437311 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + p = -1.384437311 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + p = -1.384437311 + 0.5 p = -1.384437311 + 0.5 Combine like terms: -1.384437311 + 0.5 = -0.884437311 p = -0.884437311 Simplifying p = -0.884437311Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.884437311, -0.884437311}
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