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Simplifying p2 + -14 = -12p Reorder the terms: -14 + p2 = -12p Solving -14 + p2 = -12p Solving for variable 'p'. Reorder the terms: -14 + 12p + p2 = -12p + 12p Combine like terms: -12p + 12p = 0 -14 + 12p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 12p + 14 + p2 = 0 + 14 Reorder the terms: -14 + 14 + 12p + p2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 12p + p2 = 0 + 14 12p + p2 = 0 + 14 Combine like terms: 0 + 14 = 14 12p + p2 = 14 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 = 14 + 36 Reorder the terms: 36 + 12p + p2 = 14 + 36 Combine like terms: 14 + 36 = 50 36 + 12p + p2 = 50 Factor a perfect square on the left side: (p + 6)(p + 6) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (p + 6) equal to 7.071067812 and -7.071067812.Subproblem 1
p + 6 = 7.071067812 Simplifying p + 6 = 7.071067812 Reorder the terms: 6 + p = 7.071067812 Solving 6 + p = 7.071067812 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 = 7.071067812 + -6 Combine like terms: 6 + -6 = 0 0 + p = 7.071067812 + -6 p = 7.071067812 + -6 Combine like terms: 7.071067812 + -6 = 1.071067812 p = 1.071067812 Simplifying p = 1.071067812Subproblem 2
p + 6 = -7.071067812 Simplifying p + 6 = -7.071067812 Reorder the terms: 6 + p = -7.071067812 Solving 6 + p = -7.071067812 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 = -7.071067812 + -6 Combine like terms: 6 + -6 = 0 0 + p = -7.071067812 + -6 p = -7.071067812 + -6 Combine like terms: -7.071067812 + -6 = -13.071067812 p = -13.071067812 Simplifying p = -13.071067812Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.071067812, -13.071067812}
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