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Simplifying 13p2 + 16p + -12 = 0 Reorder the terms: -12 + 16p + 13p2 = 0 Solving -12 + 16p + 13p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.9230769231 + 1.230769231p + p2 = 0 Move the constant term to the right: Add '0.9230769231' to each side of the equation. -0.9230769231 + 1.230769231p + 0.9230769231 + p2 = 0 + 0.9230769231 Reorder the terms: -0.9230769231 + 0.9230769231 + 1.230769231p + p2 = 0 + 0.9230769231 Combine like terms: -0.9230769231 + 0.9230769231 = 0.0000000000 0.0000000000 + 1.230769231p + p2 = 0 + 0.9230769231 1.230769231p + p2 = 0 + 0.9230769231 Combine like terms: 0 + 0.9230769231 = 0.9230769231 1.230769231p + p2 = 0.9230769231 The p term is 1.230769231p. Take half its coefficient (0.6153846155). Square it (0.3786982250) and add it to both sides. Add '0.3786982250' to each side of the equation. 1.230769231p + 0.3786982250 + p2 = 0.9230769231 + 0.3786982250 Reorder the terms: 0.3786982250 + 1.230769231p + p2 = 0.9230769231 + 0.3786982250 Combine like terms: 0.9230769231 + 0.3786982250 = 1.3017751481 0.3786982250 + 1.230769231p + p2 = 1.3017751481 Factor a perfect square on the left side: (p + 0.6153846155)(p + 0.6153846155) = 1.3017751481 Calculate the square root of the right side: 1.140953613 Break this problem into two subproblems by setting (p + 0.6153846155) equal to 1.140953613 and -1.140953613.Subproblem 1
p + 0.6153846155 = 1.140953613 Simplifying p + 0.6153846155 = 1.140953613 Reorder the terms: 0.6153846155 + p = 1.140953613 Solving 0.6153846155 + p = 1.140953613 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.6153846155' to each side of the equation. 0.6153846155 + -0.6153846155 + p = 1.140953613 + -0.6153846155 Combine like terms: 0.6153846155 + -0.6153846155 = 0.0000000000 0.0000000000 + p = 1.140953613 + -0.6153846155 p = 1.140953613 + -0.6153846155 Combine like terms: 1.140953613 + -0.6153846155 = 0.5255689975 p = 0.5255689975 Simplifying p = 0.5255689975Subproblem 2
p + 0.6153846155 = -1.140953613 Simplifying p + 0.6153846155 = -1.140953613 Reorder the terms: 0.6153846155 + p = -1.140953613 Solving 0.6153846155 + p = -1.140953613 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.6153846155' to each side of the equation. 0.6153846155 + -0.6153846155 + p = -1.140953613 + -0.6153846155 Combine like terms: 0.6153846155 + -0.6153846155 = 0.0000000000 0.0000000000 + p = -1.140953613 + -0.6153846155 p = -1.140953613 + -0.6153846155 Combine like terms: -1.140953613 + -0.6153846155 = -1.7563382285 p = -1.7563382285 Simplifying p = -1.7563382285Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.5255689975, -1.7563382285}
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