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Simplifying p2 + 3p = -0.4 Reorder the terms: 3p + p2 = -0.4 Solving 3p + p2 = -0.4 Solving for variable 'p'. Reorder the terms: 0.4 + 3p + p2 = -0.4 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.4 + 3p + p2 = 0.0 Begin completing the square. 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 = -0.139852949 p = -0.139852949 Simplifying p = -0.139852949Subproblem 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 = -2.860147051 p = -2.860147051 Simplifying p = -2.860147051Solution
The solution to the problem is based on the solutions from the subproblems. p = {-0.139852949, -2.860147051}
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