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Simplifying 0 = 5p2 + 27p + -12 Reorder the terms: 0 = -12 + 27p + 5p2 Solving 0 = -12 + 27p + 5p2 Solving for variable 'p'. Combine like terms: 0 + 12 = 12 12 + -27p + -5p2 = -12 + 27p + 5p2 + 12 + -27p + -5p2 Reorder the terms: 12 + -27p + -5p2 = -12 + 12 + 27p + -27p + 5p2 + -5p2 Combine like terms: -12 + 12 = 0 12 + -27p + -5p2 = 0 + 27p + -27p + 5p2 + -5p2 12 + -27p + -5p2 = 27p + -27p + 5p2 + -5p2 Combine like terms: 27p + -27p = 0 12 + -27p + -5p2 = 0 + 5p2 + -5p2 12 + -27p + -5p2 = 5p2 + -5p2 Combine like terms: 5p2 + -5p2 = 0 12 + -27p + -5p2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -2.4 + 5.4p + p2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 5.4p + 2.4 + p2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 5.4p + p2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 5.4p + p2 = 0 + 2.4 5.4p + p2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 5.4p + p2 = 2.4 The p term is 5.4p. Take half its coefficient (2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. 5.4p + 7.29 + p2 = 2.4 + 7.29 Reorder the terms: 7.29 + 5.4p + p2 = 2.4 + 7.29 Combine like terms: 2.4 + 7.29 = 9.69 7.29 + 5.4p + p2 = 9.69 Factor a perfect square on the left side: (p + 2.7)(p + 2.7) = 9.69 Calculate the square root of the right side: 3.112876483 Break this problem into two subproblems by setting (p + 2.7) equal to 3.112876483 and -3.112876483.Subproblem 1
p + 2.7 = 3.112876483 Simplifying p + 2.7 = 3.112876483 Reorder the terms: 2.7 + p = 3.112876483 Solving 2.7 + p = 3.112876483 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + p = 3.112876483 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + p = 3.112876483 + -2.7 p = 3.112876483 + -2.7 Combine like terms: 3.112876483 + -2.7 = 0.412876483 p = 0.412876483 Simplifying p = 0.412876483Subproblem 2
p + 2.7 = -3.112876483 Simplifying p + 2.7 = -3.112876483 Reorder the terms: 2.7 + p = -3.112876483 Solving 2.7 + p = -3.112876483 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2.7' to each side of the equation. 2.7 + -2.7 + p = -3.112876483 + -2.7 Combine like terms: 2.7 + -2.7 = 0.0 0.0 + p = -3.112876483 + -2.7 p = -3.112876483 + -2.7 Combine like terms: -3.112876483 + -2.7 = -5.812876483 p = -5.812876483 Simplifying p = -5.812876483Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.412876483, -5.812876483}
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