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Simplifying 5P2 + -8P + -25 = 0 Reorder the terms: -25 + -8P + 5P2 = 0 Solving -25 + -8P + 5P2 = 0 Solving for variable 'P'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5 + -1.6P + P2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -1.6P + 5 + P2 = 0 + 5 Reorder the terms: -5 + 5 + -1.6P + P2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1.6P + P2 = 0 + 5 -1.6P + P2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1.6P + P2 = 5 The P term is -1.6P. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6P + 0.64 + P2 = 5 + 0.64 Reorder the terms: 0.64 + -1.6P + P2 = 5 + 0.64 Combine like terms: 5 + 0.64 = 5.64 0.64 + -1.6P + P2 = 5.64 Factor a perfect square on the left side: (P + -0.8)(P + -0.8) = 5.64 Calculate the square root of the right side: 2.374868417 Break this problem into two subproblems by setting (P + -0.8) equal to 2.374868417 and -2.374868417.Subproblem 1
P + -0.8 = 2.374868417 Simplifying P + -0.8 = 2.374868417 Reorder the terms: -0.8 + P = 2.374868417 Solving -0.8 + P = 2.374868417 Solving for variable 'P'. Move all terms containing P to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + P = 2.374868417 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + P = 2.374868417 + 0.8 P = 2.374868417 + 0.8 Combine like terms: 2.374868417 + 0.8 = 3.174868417 P = 3.174868417 Simplifying P = 3.174868417Subproblem 2
P + -0.8 = -2.374868417 Simplifying P + -0.8 = -2.374868417 Reorder the terms: -0.8 + P = -2.374868417 Solving -0.8 + P = -2.374868417 Solving for variable 'P'. Move all terms containing P to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + P = -2.374868417 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + P = -2.374868417 + 0.8 P = -2.374868417 + 0.8 Combine like terms: -2.374868417 + 0.8 = -1.574868417 P = -1.574868417 Simplifying P = -1.574868417Solution
The solution to the problem is based on the solutions from the subproblems. P = {3.174868417, -1.574868417}
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