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Simplifying p2 + -12p = 10 Reorder the terms: -12p + p2 = 10 Solving -12p + p2 = 10 Solving for variable 'p'. Reorder the terms: -10 + -12p + p2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -12p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -12p + 10 + p2 = 0 + 10 Reorder the terms: -10 + 10 + -12p + p2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -12p + p2 = 0 + 10 -12p + p2 = 0 + 10 Combine like terms: 0 + 10 = 10 -12p + p2 = 10 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 = 10 + 36 Reorder the terms: 36 + -12p + p2 = 10 + 36 Combine like terms: 10 + 36 = 46 36 + -12p + p2 = 46 Factor a perfect square on the left side: (p + -6)(p + -6) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (p + -6) equal to 6.782329983 and -6.782329983.Subproblem 1
p + -6 = 6.782329983 Simplifying p + -6 = 6.782329983 Reorder the terms: -6 + p = 6.782329983 Solving -6 + p = 6.782329983 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 = 6.782329983 + 6 Combine like terms: -6 + 6 = 0 0 + p = 6.782329983 + 6 p = 6.782329983 + 6 Combine like terms: 6.782329983 + 6 = 12.782329983 p = 12.782329983 Simplifying p = 12.782329983Subproblem 2
p + -6 = -6.782329983 Simplifying p + -6 = -6.782329983 Reorder the terms: -6 + p = -6.782329983 Solving -6 + p = -6.782329983 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 = -6.782329983 + 6 Combine like terms: -6 + 6 = 0 0 + p = -6.782329983 + 6 p = -6.782329983 + 6 Combine like terms: -6.782329983 + 6 = -0.782329983 p = -0.782329983 Simplifying p = -0.782329983Solution
The solution to the problem is based on the solutions from the subproblems. p = {12.782329983, -0.782329983}
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