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Simplifying 3p + -1p2 = 0.4 Solving 3p + -1p2 = 0.4 Solving for variable 'p'. Reorder the terms: -0.4 + 3p + -1p2 = 0.4 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 -0.4 + 3p + -1p2 = 0.0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.4 + -3p + p2 = 0.0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -3p + -0.4 + p2 = 0.0 + -0.4 Reorder the terms: 0.4 + -0.4 + -3p + p2 = 0.0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -3p + p2 = 0.0 + -0.4 -3p + p2 = 0.0 + -0.4 Combine like terms: 0.0 + -0.4 = -0.4 -3p + p2 = -0.4 The p term is -3p. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3p + 2.25 + p2 = -0.4 + 2.25 Reorder the terms: 2.25 + -3p + p2 = -0.4 + 2.25 Combine like terms: -0.4 + 2.25 = 1.85 2.25 + -3p + p2 = 1.85 Factor a perfect square on the left side: (p + -1.5)(p + -1.5) = 1.85 Calculate the square root of the right side: 1.360147051 Break this problem into two subproblems by setting (p + -1.5) equal to 1.360147051 and -1.360147051.Subproblem 1
p + -1.5 = 1.360147051 Simplifying p + -1.5 = 1.360147051 Reorder the terms: -1.5 + p = 1.360147051 Solving -1.5 + p = 1.360147051 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = 1.360147051 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = 1.360147051 + 1.5 p = 1.360147051 + 1.5 Combine like terms: 1.360147051 + 1.5 = 2.860147051 p = 2.860147051 Simplifying p = 2.860147051Subproblem 2
p + -1.5 = -1.360147051 Simplifying p + -1.5 = -1.360147051 Reorder the terms: -1.5 + p = -1.360147051 Solving -1.5 + p = -1.360147051 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + p = -1.360147051 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + p = -1.360147051 + 1.5 p = -1.360147051 + 1.5 Combine like terms: -1.360147051 + 1.5 = 0.139852949 p = 0.139852949 Simplifying p = 0.139852949Solution
The solution to the problem is based on the solutions from the subproblems. p = {2.860147051, 0.139852949}
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