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Simplifying 10p2 + -11p + 2 = 0 Reorder the terms: 2 + -11p + 10p2 = 0 Solving 2 + -11p + 10p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.2 + -1.1p + p2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -1.1p + -0.2 + p2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -1.1p + p2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -1.1p + p2 = 0 + -0.2 -1.1p + p2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -1.1p + p2 = -0.2 The p term is -1.1p. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1p + 0.3025 + p2 = -0.2 + 0.3025 Reorder the terms: 0.3025 + -1.1p + p2 = -0.2 + 0.3025 Combine like terms: -0.2 + 0.3025 = 0.1025 0.3025 + -1.1p + p2 = 0.1025 Factor a perfect square on the left side: (p + -0.55)(p + -0.55) = 0.1025 Calculate the square root of the right side: 0.320156212 Break this problem into two subproblems by setting (p + -0.55) equal to 0.320156212 and -0.320156212.Subproblem 1
p + -0.55 = 0.320156212 Simplifying p + -0.55 = 0.320156212 Reorder the terms: -0.55 + p = 0.320156212 Solving -0.55 + p = 0.320156212 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + p = 0.320156212 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + p = 0.320156212 + 0.55 p = 0.320156212 + 0.55 Combine like terms: 0.320156212 + 0.55 = 0.870156212 p = 0.870156212 Simplifying p = 0.870156212Subproblem 2
p + -0.55 = -0.320156212 Simplifying p + -0.55 = -0.320156212 Reorder the terms: -0.55 + p = -0.320156212 Solving -0.55 + p = -0.320156212 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + p = -0.320156212 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + p = -0.320156212 + 0.55 p = -0.320156212 + 0.55 Combine like terms: -0.320156212 + 0.55 = 0.229843788 p = 0.229843788 Simplifying p = 0.229843788Solution
The solution to the problem is based on the solutions from the subproblems. p = {0.870156212, 0.229843788}
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