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Simplifying 7p2 + 7p = -1 Reorder the terms: 7p + 7p2 = -1 Solving 7p + 7p2 = -1 Solving for variable 'p'. Reorder the terms: 1 + 7p + 7p2 = -1 + 1 Combine like terms: -1 + 1 = 0 1 + 7p + 7p2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + p + p2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + p + -0.1428571429 + p2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + p + p2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + p + p2 = 0 + -0.1428571429 p + p2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 p + p2 = -0.1428571429 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. + 0.25 + p2 = -0.1428571429 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + p2 = -0.1428571429 + 0.25 Combine like terms: -0.1428571429 + 0.25 = 0.1071428571 1.25 + p2 = 0.1071428571 Factor a perfect square on the left side: (p + 0.5)(p + 0.5) = 0.1071428571 Calculate the square root of the right side: 0.327326835 Break this problem into two subproblems by setting (p + 0.5) equal to 0.327326835 and -0.327326835.Subproblem 1
p + 0.5 = 0.327326835 Simplifying p + 0.5 = 0.327326835 Reorder the terms: 0.5 + p = 0.327326835 Solving 0.5 + p = 0.327326835 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 = 0.327326835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = 0.327326835 + -0.5 p = 0.327326835 + -0.5 Combine like terms: 0.327326835 + -0.5 = -0.172673165 p = -0.172673165 Simplifying p = -0.172673165Subproblem 2
p + 0.5 = -0.327326835 Simplifying p + 0.5 = -0.327326835 Reorder the terms: 0.5 + p = -0.327326835 Solving 0.5 + p = -0.327326835 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 = -0.327326835 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + p = -0.327326835 + -0.5 p = -0.327326835 + -0.5 Combine like terms: -0.327326835 + -0.5 = -0.827326835 p = -0.827326835 Simplifying p = -0.827326835Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.172673165, -0.827326835}
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