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Simplifying x2 + -19x + -596.4 = 0 Reorder the terms: -596.4 + -19x + x2 = 0 Solving -596.4 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '596.4' to each side of the equation. -596.4 + -19x + 596.4 + x2 = 0 + 596.4 Reorder the terms: -596.4 + 596.4 + -19x + x2 = 0 + 596.4 Combine like terms: -596.4 + 596.4 = 0.0 0.0 + -19x + x2 = 0 + 596.4 -19x + x2 = 0 + 596.4 Combine like terms: 0 + 596.4 = 596.4 -19x + x2 = 596.4 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 596.4 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 596.4 + 90.25 Combine like terms: 596.4 + 90.25 = 686.65 90.25 + -19x + x2 = 686.65 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 686.65 Calculate the square root of the right side: 26.204007327 Break this problem into two subproblems by setting (x + -9.5) equal to 26.204007327 and -26.204007327.Subproblem 1
x + -9.5 = 26.204007327 Simplifying x + -9.5 = 26.204007327 Reorder the terms: -9.5 + x = 26.204007327 Solving -9.5 + x = 26.204007327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 26.204007327 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 26.204007327 + 9.5 x = 26.204007327 + 9.5 Combine like terms: 26.204007327 + 9.5 = 35.704007327 x = 35.704007327 Simplifying x = 35.704007327Subproblem 2
x + -9.5 = -26.204007327 Simplifying x + -9.5 = -26.204007327 Reorder the terms: -9.5 + x = -26.204007327 Solving -9.5 + x = -26.204007327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -26.204007327 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -26.204007327 + 9.5 x = -26.204007327 + 9.5 Combine like terms: -26.204007327 + 9.5 = -16.704007327 x = -16.704007327 Simplifying x = -16.704007327Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.704007327, -16.704007327}
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