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Simplifying (9p2 + 7p) + (5p2 + -4p + -12) = 0 Reorder the terms: (7p + 9p2) + (5p2 + -4p + -12) = 0 Remove parenthesis around (7p + 9p2) 7p + 9p2 + (5p2 + -4p + -12) = 0 Reorder the terms: 7p + 9p2 + (-12 + -4p + 5p2) = 0 Remove parenthesis around (-12 + -4p + 5p2) 7p + 9p2 + -12 + -4p + 5p2 = 0 Reorder the terms: -12 + 7p + -4p + 9p2 + 5p2 = 0 Combine like terms: 7p + -4p = 3p -12 + 3p + 9p2 + 5p2 = 0 Combine like terms: 9p2 + 5p2 = 14p2 -12 + 3p + 14p2 = 0 Solving -12 + 3p + 14p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.8571428571 + 0.2142857143p + p2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 0.2142857143p + 0.8571428571 + p2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 0.2142857143p + p2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 0.2142857143p + p2 = 0 + 0.8571428571 0.2142857143p + p2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 0.2142857143p + p2 = 0.8571428571 The p term is 0.2142857143p. Take half its coefficient (0.1071428572). Square it (0.01147959185) and add it to both sides. Add '0.01147959185' to each side of the equation. 0.2142857143p + 0.01147959185 + p2 = 0.8571428571 + 0.01147959185 Reorder the terms: 0.01147959185 + 0.2142857143p + p2 = 0.8571428571 + 0.01147959185 Combine like terms: 0.8571428571 + 0.01147959185 = 0.86862244895 0.01147959185 + 0.2142857143p + p2 = 0.86862244895 Factor a perfect square on the left side: (p + 0.1071428572)(p + 0.1071428572) = 0.86862244895 Calculate the square root of the right side: 0.931999168 Break this problem into two subproblems by setting (p + 0.1071428572) equal to 0.931999168 and -0.931999168.Subproblem 1
p + 0.1071428572 = 0.931999168 Simplifying p + 0.1071428572 = 0.931999168 Reorder the terms: 0.1071428572 + p = 0.931999168 Solving 0.1071428572 + p = 0.931999168 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.1071428572' to each side of the equation. 0.1071428572 + -0.1071428572 + p = 0.931999168 + -0.1071428572 Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000 0.0000000000 + p = 0.931999168 + -0.1071428572 p = 0.931999168 + -0.1071428572 Combine like terms: 0.931999168 + -0.1071428572 = 0.8248563108 p = 0.8248563108 Simplifying p = 0.8248563108Subproblem 2
p + 0.1071428572 = -0.931999168 Simplifying p + 0.1071428572 = -0.931999168 Reorder the terms: 0.1071428572 + p = -0.931999168 Solving 0.1071428572 + p = -0.931999168 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.1071428572' to each side of the equation. 0.1071428572 + -0.1071428572 + p = -0.931999168 + -0.1071428572 Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000 0.0000000000 + p = -0.931999168 + -0.1071428572 p = -0.931999168 + -0.1071428572 Combine like terms: -0.931999168 + -0.1071428572 = -1.0391420252 p = -1.0391420252 Simplifying p = -1.0391420252Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.8248563108, -1.0391420252}
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