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Simplifying -12p = -1p2 + 67 Reorder the terms: -12p = 67 + -1p2 Solving -12p = 67 + -1p2 Solving for variable 'p'. Reorder the terms: -67 + -12p + p2 = 67 + -1p2 + -67 + p2 Reorder the terms: -67 + -12p + p2 = 67 + -67 + -1p2 + p2 Combine like terms: 67 + -67 = 0 -67 + -12p + p2 = 0 + -1p2 + p2 -67 + -12p + p2 = -1p2 + p2 Combine like terms: -1p2 + p2 = 0 -67 + -12p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '67' to each side of the equation. -67 + -12p + 67 + p2 = 0 + 67 Reorder the terms: -67 + 67 + -12p + p2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + -12p + p2 = 0 + 67 -12p + p2 = 0 + 67 Combine like terms: 0 + 67 = 67 -12p + p2 = 67 The p term is -12p. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12p + 36 + p2 = 67 + 36 Reorder the terms: 36 + -12p + p2 = 67 + 36 Combine like terms: 67 + 36 = 103 36 + -12p + p2 = 103 Factor a perfect square on the left side: (p + -6)(p + -6) = 103 Calculate the square root of the right side: 10.148891565 Break this problem into two subproblems by setting (p + -6) equal to 10.148891565 and -10.148891565.Subproblem 1
p + -6 = 10.148891565 Simplifying p + -6 = 10.148891565 Reorder the terms: -6 + p = 10.148891565 Solving -6 + p = 10.148891565 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + p = 10.148891565 + 6 Combine like terms: -6 + 6 = 0 0 + p = 10.148891565 + 6 p = 10.148891565 + 6 Combine like terms: 10.148891565 + 6 = 16.148891565 p = 16.148891565 Simplifying p = 16.148891565Subproblem 2
p + -6 = -10.148891565 Simplifying p + -6 = -10.148891565 Reorder the terms: -6 + p = -10.148891565 Solving -6 + p = -10.148891565 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + p = -10.148891565 + 6 Combine like terms: -6 + 6 = 0 0 + p = -10.148891565 + 6 p = -10.148891565 + 6 Combine like terms: -10.148891565 + 6 = -4.148891565 p = -4.148891565 Simplifying p = -4.148891565Solution
The solution to the problem is based on the solutions from the subproblems. p = {16.148891565, -4.148891565}
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