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Simplifying p2 + -89 = -14p Reorder the terms: -89 + p2 = -14p Solving -89 + p2 = -14p Solving for variable 'p'. Reorder the terms: -89 + 14p + p2 = -14p + 14p Combine like terms: -14p + 14p = 0 -89 + 14p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '89' to each side of the equation. -89 + 14p + 89 + p2 = 0 + 89 Reorder the terms: -89 + 89 + 14p + p2 = 0 + 89 Combine like terms: -89 + 89 = 0 0 + 14p + p2 = 0 + 89 14p + p2 = 0 + 89 Combine like terms: 0 + 89 = 89 14p + p2 = 89 The p term is 14p. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14p + 49 + p2 = 89 + 49 Reorder the terms: 49 + 14p + p2 = 89 + 49 Combine like terms: 89 + 49 = 138 49 + 14p + p2 = 138 Factor a perfect square on the left side: (p + 7)(p + 7) = 138 Calculate the square root of the right side: 11.747340124 Break this problem into two subproblems by setting (p + 7) equal to 11.747340124 and -11.747340124.Subproblem 1
p + 7 = 11.747340124 Simplifying p + 7 = 11.747340124 Reorder the terms: 7 + p = 11.747340124 Solving 7 + p = 11.747340124 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + p = 11.747340124 + -7 Combine like terms: 7 + -7 = 0 0 + p = 11.747340124 + -7 p = 11.747340124 + -7 Combine like terms: 11.747340124 + -7 = 4.747340124 p = 4.747340124 Simplifying p = 4.747340124Subproblem 2
p + 7 = -11.747340124 Simplifying p + 7 = -11.747340124 Reorder the terms: 7 + p = -11.747340124 Solving 7 + p = -11.747340124 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + p = -11.747340124 + -7 Combine like terms: 7 + -7 = 0 0 + p = -11.747340124 + -7 p = -11.747340124 + -7 Combine like terms: -11.747340124 + -7 = -18.747340124 p = -18.747340124 Simplifying p = -18.747340124Solution
The solution to the problem is based on the solutions from the subproblems. p = {4.747340124, -18.747340124}
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