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Simplifying 9p2 + -16p + 4 = 0 Reorder the terms: 4 + -16p + 9p2 = 0 Solving 4 + -16p + 9p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + -1.777777778p + p2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -1.777777778p + -0.4444444444 + p2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -1.777777778p + p2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -1.777777778p + p2 = 0 + -0.4444444444 -1.777777778p + p2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -1.777777778p + p2 = -0.4444444444 The p term is -1.777777778p. Take half its coefficient (-0.888888889). Square it (0.7901234570) and add it to both sides. Add '0.7901234570' to each side of the equation. -1.777777778p + 0.7901234570 + p2 = -0.4444444444 + 0.7901234570 Reorder the terms: 0.7901234570 + -1.777777778p + p2 = -0.4444444444 + 0.7901234570 Combine like terms: -0.4444444444 + 0.7901234570 = 0.3456790126 0.7901234570 + -1.777777778p + p2 = 0.3456790126 Factor a perfect square on the left side: (p + -0.888888889)(p + -0.888888889) = 0.3456790126 Calculate the square root of the right side: 0.587944736 Break this problem into two subproblems by setting (p + -0.888888889) equal to 0.587944736 and -0.587944736.Subproblem 1
p + -0.888888889 = 0.587944736 Simplifying p + -0.888888889 = 0.587944736 Reorder the terms: -0.888888889 + p = 0.587944736 Solving -0.888888889 + p = 0.587944736 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + p = 0.587944736 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + p = 0.587944736 + 0.888888889 p = 0.587944736 + 0.888888889 Combine like terms: 0.587944736 + 0.888888889 = 1.476833625 p = 1.476833625 Simplifying p = 1.476833625Subproblem 2
p + -0.888888889 = -0.587944736 Simplifying p + -0.888888889 = -0.587944736 Reorder the terms: -0.888888889 + p = -0.587944736 Solving -0.888888889 + p = -0.587944736 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.888888889' to each side of the equation. -0.888888889 + 0.888888889 + p = -0.587944736 + 0.888888889 Combine like terms: -0.888888889 + 0.888888889 = 0.000000000 0.000000000 + p = -0.587944736 + 0.888888889 p = -0.587944736 + 0.888888889 Combine like terms: -0.587944736 + 0.888888889 = 0.300944153 p = 0.300944153 Simplifying p = 0.300944153Solution
The solution to the problem is based on the solutions from the subproblems. p = {1.476833625, 0.300944153}
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