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Simplifying 0.29p2 + -0.38p + -3 = 0 Reorder the terms: -3 + -0.38p + 0.29p2 = 0 Solving -3 + -0.38p + 0.29p2 = 0 Solving for variable 'p'. Begin completing the square. Divide all terms by 0.29 the coefficient of the squared term: Divide each side by '0.29'. -10.34482759 + -1.310344828p + p2 = 0 Move the constant term to the right: Add '10.34482759' to each side of the equation. -10.34482759 + -1.310344828p + 10.34482759 + p2 = 0 + 10.34482759 Reorder the terms: -10.34482759 + 10.34482759 + -1.310344828p + p2 = 0 + 10.34482759 Combine like terms: -10.34482759 + 10.34482759 = 0.00000000 0.00000000 + -1.310344828p + p2 = 0 + 10.34482759 -1.310344828p + p2 = 0 + 10.34482759 Combine like terms: 0 + 10.34482759 = 10.34482759 -1.310344828p + p2 = 10.34482759 The p term is -1.310344828p. Take half its coefficient (-0.655172414). Square it (0.4292508921) and add it to both sides. Add '0.4292508921' to each side of the equation. -1.310344828p + 0.4292508921 + p2 = 10.34482759 + 0.4292508921 Reorder the terms: 0.4292508921 + -1.310344828p + p2 = 10.34482759 + 0.4292508921 Combine like terms: 10.34482759 + 0.4292508921 = 10.7740784821 0.4292508921 + -1.310344828p + p2 = 10.7740784821 Factor a perfect square on the left side: (p + -0.655172414)(p + -0.655172414) = 10.7740784821 Calculate the square root of the right side: 3.282389142 Break this problem into two subproblems by setting (p + -0.655172414) equal to 3.282389142 and -3.282389142.Subproblem 1
p + -0.655172414 = 3.282389142 Simplifying p + -0.655172414 = 3.282389142 Reorder the terms: -0.655172414 + p = 3.282389142 Solving -0.655172414 + p = 3.282389142 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.655172414' to each side of the equation. -0.655172414 + 0.655172414 + p = 3.282389142 + 0.655172414 Combine like terms: -0.655172414 + 0.655172414 = 0.000000000 0.000000000 + p = 3.282389142 + 0.655172414 p = 3.282389142 + 0.655172414 Combine like terms: 3.282389142 + 0.655172414 = 3.937561556 p = 3.937561556 Simplifying p = 3.937561556Subproblem 2
p + -0.655172414 = -3.282389142 Simplifying p + -0.655172414 = -3.282389142 Reorder the terms: -0.655172414 + p = -3.282389142 Solving -0.655172414 + p = -3.282389142 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '0.655172414' to each side of the equation. -0.655172414 + 0.655172414 + p = -3.282389142 + 0.655172414 Combine like terms: -0.655172414 + 0.655172414 = 0.000000000 0.000000000 + p = -3.282389142 + 0.655172414 p = -3.282389142 + 0.655172414 Combine like terms: -3.282389142 + 0.655172414 = -2.627216728 p = -2.627216728 Simplifying p = -2.627216728Solution
The solution to the problem is based on the solutions from the subproblems. p = {3.937561556, -2.627216728}
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