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Simplifying 7p2 + -2p + -2 = 0 Reorder the terms: -2 + -2p + 7p2 = 0 Solving -2 + -2p + 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 + -0.2857142857p + p2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -0.2857142857p + 0.2857142857 + p2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -0.2857142857p + p2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -0.2857142857p + p2 = 0 + 0.2857142857 -0.2857142857p + p2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -0.2857142857p + p2 = 0.2857142857 The p term is -0.2857142857p. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857p + 0.02040816328 + p2 = 0.2857142857 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857p + p2 = 0.2857142857 + 0.02040816328 Combine like terms: 0.2857142857 + 0.02040816328 = 0.30612244898 0.02040816328 + -0.2857142857p + p2 = 0.30612244898 Factor a perfect square on the left side: (p + -0.1428571429)(p + -0.1428571429) = 0.30612244898 Calculate the square root of the right side: 0.553283335 Break this problem into two subproblems by setting (p + -0.1428571429) equal to 0.553283335 and -0.553283335.Subproblem 1
p + -0.1428571429 = 0.553283335 Simplifying p + -0.1428571429 = 0.553283335 Reorder the terms: -0.1428571429 + p = 0.553283335 Solving -0.1428571429 + p = 0.553283335 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + p = 0.553283335 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + p = 0.553283335 + 0.1428571429 p = 0.553283335 + 0.1428571429 Combine like terms: 0.553283335 + 0.1428571429 = 0.6961404779 p = 0.6961404779 Simplifying p = 0.6961404779Subproblem 2
p + -0.1428571429 = -0.553283335 Simplifying p + -0.1428571429 = -0.553283335 Reorder the terms: -0.1428571429 + p = -0.553283335 Solving -0.1428571429 + p = -0.553283335 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + p = -0.553283335 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + p = -0.553283335 + 0.1428571429 p = -0.553283335 + 0.1428571429 Combine like terms: -0.553283335 + 0.1428571429 = -0.4104261921 p = -0.4104261921 Simplifying p = -0.4104261921Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.6961404779, -0.4104261921}
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