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Simplifying 3p2 + 12p + -2510 = 0 Reorder the terms: -2510 + 12p + 3p2 = 0 Solving -2510 + 12p + 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'. -836.6666667 + 4p + p2 = 0 Move the constant term to the right: Add '836.6666667' to each side of the equation. -836.6666667 + 4p + 836.6666667 + p2 = 0 + 836.6666667 Reorder the terms: -836.6666667 + 836.6666667 + 4p + p2 = 0 + 836.6666667 Combine like terms: -836.6666667 + 836.6666667 = 0.0000000 0.0000000 + 4p + p2 = 0 + 836.6666667 4p + p2 = 0 + 836.6666667 Combine like terms: 0 + 836.6666667 = 836.6666667 4p + p2 = 836.6666667 The p term is 4p. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4p + 4 + p2 = 836.6666667 + 4 Reorder the terms: 4 + 4p + p2 = 836.6666667 + 4 Combine like terms: 836.6666667 + 4 = 840.6666667 4 + 4p + p2 = 840.6666667 Factor a perfect square on the left side: (p + 2)(p + 2) = 840.6666667 Calculate the square root of the right side: 28.994252305 Break this problem into two subproblems by setting (p + 2) equal to 28.994252305 and -28.994252305.Subproblem 1
p + 2 = 28.994252305 Simplifying p + 2 = 28.994252305 Reorder the terms: 2 + p = 28.994252305 Solving 2 + p = 28.994252305 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = 28.994252305 + -2 Combine like terms: 2 + -2 = 0 0 + p = 28.994252305 + -2 p = 28.994252305 + -2 Combine like terms: 28.994252305 + -2 = 26.994252305 p = 26.994252305 Simplifying p = 26.994252305Subproblem 2
p + 2 = -28.994252305 Simplifying p + 2 = -28.994252305 Reorder the terms: 2 + p = -28.994252305 Solving 2 + p = -28.994252305 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + p = -28.994252305 + -2 Combine like terms: 2 + -2 = 0 0 + p = -28.994252305 + -2 p = -28.994252305 + -2 Combine like terms: -28.994252305 + -2 = -30.994252305 p = -30.994252305 Simplifying p = -30.994252305Solution
The solution to the problem is based on the solutions from the subproblems. p = {26.994252305, -30.994252305}
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