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Simplifying 0.9p2 + -8p + 3.3 + -2 = 0 Reorder the terms: 3.3 + -2 + -8p + 0.9p2 = 0 Combine like terms: 3.3 + -2 = 1.3 1.3 + -8p + 0.9p2 = 0 Solving 1.3 + -8p + 0.9p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 0.9 the coefficient of the squared term: Divide each side by '0.9'. 1.444444444 + -8.888888889p + p2 = 0 Move the constant term to the right: Add '-1.444444444' to each side of the equation. 1.444444444 + -8.888888889p + -1.444444444 + p2 = 0 + -1.444444444 Reorder the terms: 1.444444444 + -1.444444444 + -8.888888889p + p2 = 0 + -1.444444444 Combine like terms: 1.444444444 + -1.444444444 = 0.000000000 0.000000000 + -8.888888889p + p2 = 0 + -1.444444444 -8.888888889p + p2 = 0 + -1.444444444 Combine like terms: 0 + -1.444444444 = -1.444444444 -8.888888889p + p2 = -1.444444444 The p term is -8.888888889p. Take half its coefficient (-4.444444445). Square it (19.75308642) and add it to both sides. Add '19.75308642' to each side of the equation. -8.888888889p + 19.75308642 + p2 = -1.444444444 + 19.75308642 Reorder the terms: 19.75308642 + -8.888888889p + p2 = -1.444444444 + 19.75308642 Combine like terms: -1.444444444 + 19.75308642 = 18.308641976 19.75308642 + -8.888888889p + p2 = 18.308641976 Factor a perfect square on the left side: (p + -4.444444445)(p + -4.444444445) = 18.308641976 Calculate the square root of the right side: 4.278859892 Break this problem into two subproblems by setting (p + -4.444444445) equal to 4.278859892 and -4.278859892.Subproblem 1
p + -4.444444445 = 4.278859892 Simplifying p + -4.444444445 = 4.278859892 Reorder the terms: -4.444444445 + p = 4.278859892 Solving -4.444444445 + p = 4.278859892 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + p = 4.278859892 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + p = 4.278859892 + 4.444444445 p = 4.278859892 + 4.444444445 Combine like terms: 4.278859892 + 4.444444445 = 8.723304337 p = 8.723304337 Simplifying p = 8.723304337Subproblem 2
p + -4.444444445 = -4.278859892 Simplifying p + -4.444444445 = -4.278859892 Reorder the terms: -4.444444445 + p = -4.278859892 Solving -4.444444445 + p = -4.278859892 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + p = -4.278859892 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + p = -4.278859892 + 4.444444445 p = -4.278859892 + 4.444444445 Combine like terms: -4.278859892 + 4.444444445 = 0.165584553 p = 0.165584553 Simplifying p = 0.165584553Solution
The solution to the problem is based on the solutions from the subproblems. p = {8.723304337, 0.165584553}
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