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Simplifying 0 = p2 + -8p + -14 Reorder the terms: 0 = -14 + -8p + p2 Solving 0 = -14 + -8p + p2 Solving for variable 'p'. Combine like terms: 0 + 14 = 14 14 + 8p + -1p2 = -14 + -8p + p2 + 14 + 8p + -1p2 Reorder the terms: 14 + 8p + -1p2 = -14 + 14 + -8p + 8p + p2 + -1p2 Combine like terms: -14 + 14 = 0 14 + 8p + -1p2 = 0 + -8p + 8p + p2 + -1p2 14 + 8p + -1p2 = -8p + 8p + p2 + -1p2 Combine like terms: -8p + 8p = 0 14 + 8p + -1p2 = 0 + p2 + -1p2 14 + 8p + -1p2 = p2 + -1p2 Combine like terms: p2 + -1p2 = 0 14 + 8p + -1p2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -14 + -8p + p2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -8p + 14 + p2 = 0 + 14 Reorder the terms: -14 + 14 + -8p + p2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -8p + p2 = 0 + 14 -8p + p2 = 0 + 14 Combine like terms: 0 + 14 = 14 -8p + p2 = 14 The p term is -8p. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8p + 16 + p2 = 14 + 16 Reorder the terms: 16 + -8p + p2 = 14 + 16 Combine like terms: 14 + 16 = 30 16 + -8p + p2 = 30 Factor a perfect square on the left side: (p + -4)(p + -4) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (p + -4) equal to 5.477225575 and -5.477225575.Subproblem 1
p + -4 = 5.477225575 Simplifying p + -4 = 5.477225575 Reorder the terms: -4 + p = 5.477225575 Solving -4 + p = 5.477225575 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = 5.477225575 + 4 Combine like terms: -4 + 4 = 0 0 + p = 5.477225575 + 4 p = 5.477225575 + 4 Combine like terms: 5.477225575 + 4 = 9.477225575 p = 9.477225575 Simplifying p = 9.477225575Subproblem 2
p + -4 = -5.477225575 Simplifying p + -4 = -5.477225575 Reorder the terms: -4 + p = -5.477225575 Solving -4 + p = -5.477225575 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = -5.477225575 + 4 Combine like terms: -4 + 4 = 0 0 + p = -5.477225575 + 4 p = -5.477225575 + 4 Combine like terms: -5.477225575 + 4 = -1.477225575 p = -1.477225575 Simplifying p = -1.477225575Solution
The solution to the problem is based on the solutions from the subproblems. p = {9.477225575, -1.477225575}
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