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Simplifying 7p2 + 16p + 2 = 0 Reorder the terms: 2 + 16p + 7p2 = 0 Solving 2 + 16p + 7p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + 2.285714286p + p2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 2.285714286p + -0.2857142857 + p2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 2.285714286p + p2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 2.285714286p + p2 = 0 + -0.2857142857 2.285714286p + p2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 2.285714286p + p2 = -0.2857142857 The p term is 2.285714286p. Take half its coefficient (1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. 2.285714286p + 1.306122449 + p2 = -0.2857142857 + 1.306122449 Reorder the terms: 1.306122449 + 2.285714286p + p2 = -0.2857142857 + 1.306122449 Combine like terms: -0.2857142857 + 1.306122449 = 1.0204081633 1.306122449 + 2.285714286p + p2 = 1.0204081633 Factor a perfect square on the left side: (p + 1.142857143)(p + 1.142857143) = 1.0204081633 Calculate the square root of the right side: 1.010152545 Break this problem into two subproblems by setting (p + 1.142857143) equal to 1.010152545 and -1.010152545.Subproblem 1
p + 1.142857143 = 1.010152545 Simplifying p + 1.142857143 = 1.010152545 Reorder the terms: 1.142857143 + p = 1.010152545 Solving 1.142857143 + p = 1.010152545 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + p = 1.010152545 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + p = 1.010152545 + -1.142857143 p = 1.010152545 + -1.142857143 Combine like terms: 1.010152545 + -1.142857143 = -0.132704598 p = -0.132704598 Simplifying p = -0.132704598Subproblem 2
p + 1.142857143 = -1.010152545 Simplifying p + 1.142857143 = -1.010152545 Reorder the terms: 1.142857143 + p = -1.010152545 Solving 1.142857143 + p = -1.010152545 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + p = -1.010152545 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + p = -1.010152545 + -1.142857143 p = -1.010152545 + -1.142857143 Combine like terms: -1.010152545 + -1.142857143 = -2.153009688 p = -2.153009688 Simplifying p = -2.153009688Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.132704598, -2.153009688}
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