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Simplifying p2 + 2p + 1 + -6p = 85 Reorder the terms: 1 + 2p + -6p + p2 = 85 Combine like terms: 2p + -6p = -4p 1 + -4p + p2 = 85 Solving 1 + -4p + p2 = 85 Solving for variable 'p'. Reorder the terms: 1 + -85 + -4p + p2 = 85 + -85 Combine like terms: 1 + -85 = -84 -84 + -4p + p2 = 85 + -85 Combine like terms: 85 + -85 = 0 -84 + -4p + p2 = 0 Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + -4p + 84 + p2 = 0 + 84 Reorder the terms: -84 + 84 + -4p + p2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + -4p + p2 = 0 + 84 -4p + p2 = 0 + 84 Combine like terms: 0 + 84 = 84 -4p + p2 = 84 The p term is -4p. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4p + 4 + p2 = 84 + 4 Reorder the terms: 4 + -4p + p2 = 84 + 4 Combine like terms: 84 + 4 = 88 4 + -4p + p2 = 88 Factor a perfect square on the left side: (p + -2)(p + -2) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (p + -2) equal to 9.38083152 and -9.38083152.Subproblem 1
p + -2 = 9.38083152 Simplifying p + -2 = 9.38083152 Reorder the terms: -2 + p = 9.38083152 Solving -2 + p = 9.38083152 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = 9.38083152 + 2 Combine like terms: -2 + 2 = 0 0 + p = 9.38083152 + 2 p = 9.38083152 + 2 Combine like terms: 9.38083152 + 2 = 11.38083152 p = 11.38083152 Simplifying p = 11.38083152Subproblem 2
p + -2 = -9.38083152 Simplifying p + -2 = -9.38083152 Reorder the terms: -2 + p = -9.38083152 Solving -2 + p = -9.38083152 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + p = -9.38083152 + 2 Combine like terms: -2 + 2 = 0 0 + p = -9.38083152 + 2 p = -9.38083152 + 2 Combine like terms: -9.38083152 + 2 = -7.38083152 p = -7.38083152 Simplifying p = -7.38083152Solution
The solution to the problem is based on the solutions from the subproblems. p = {11.38083152, -7.38083152}
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