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Simplifying -7p2 + p + 5 = 0 Reorder the terms: 5 + p + -7p2 = 0 Solving 5 + p + -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'. -0.7142857143 + -0.1428571429p + p2 = 0 Move the constant term to the right: Add '0.7142857143' to each side of the equation. -0.7142857143 + -0.1428571429p + 0.7142857143 + p2 = 0 + 0.7142857143 Reorder the terms: -0.7142857143 + 0.7142857143 + -0.1428571429p + p2 = 0 + 0.7142857143 Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000 0.0000000000 + -0.1428571429p + p2 = 0 + 0.7142857143 -0.1428571429p + p2 = 0 + 0.7142857143 Combine like terms: 0 + 0.7142857143 = 0.7142857143 -0.1428571429p + p2 = 0.7142857143 The p term is p. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.1428571429p + 0.25 + p2 = 0.7142857143 + 0.25 Reorder the terms: 0.25 + -0.1428571429p + p2 = 0.7142857143 + 0.25 Combine like terms: 0.7142857143 + 0.25 = 0.9642857143 0.25 + -0.1428571429p + p2 = 0.9642857143 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 0.9642857143 Calculate the square root of the right side: 0.981980506 Break this problem into two subproblems by setting (p + 0.5) equal to 0.981980506 and -0.981980506.Subproblem 1
p + 0.5 = 0.981980506 Simplifying p + 0.5 = 0.981980506 Reorder the terms: 0.5 + p = 0.981980506 Solving 0.5 + p = 0.981980506 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = 0.981980506 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 0.981980506 + -0.5 p = 0.981980506 + -0.5 Combine like terms: 0.981980506 + -0.5 = 0.481980506 p = 0.481980506 Simplifying p = 0.481980506Subproblem 2
p + 0.5 = -0.981980506 Simplifying p + 0.5 = -0.981980506 Reorder the terms: 0.5 + p = -0.981980506 Solving 0.5 + p = -0.981980506 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + p = -0.981980506 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -0.981980506 + -0.5 p = -0.981980506 + -0.5 Combine like terms: -0.981980506 + -0.5 = -1.481980506 p = -1.481980506 Simplifying p = -1.481980506Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.481980506, -1.481980506}
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