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Simplifying x2 + -1x + -86 = 0 Reorder the terms: -86 + -1x + x2 = 0 Solving -86 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '86' to each side of the equation. -86 + -1x + 86 + x2 = 0 + 86 Reorder the terms: -86 + 86 + -1x + x2 = 0 + 86 Combine like terms: -86 + 86 = 0 0 + -1x + x2 = 0 + 86 -1x + x2 = 0 + 86 Combine like terms: 0 + 86 = 86 -1x + x2 = 86 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 86 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 86 + 0.25 Combine like terms: 86 + 0.25 = 86.25 0.25 + -1x + x2 = 86.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 86.25 Calculate the square root of the right side: 9.287087811 Break this problem into two subproblems by setting (x + -0.5) equal to 9.287087811 and -9.287087811.Subproblem 1
x + -0.5 = 9.287087811 Simplifying x + -0.5 = 9.287087811 Reorder the terms: -0.5 + x = 9.287087811 Solving -0.5 + x = 9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 9.287087811 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 9.287087811 + 0.5 x = 9.287087811 + 0.5 Combine like terms: 9.287087811 + 0.5 = 9.787087811 x = 9.787087811 Simplifying x = 9.787087811Subproblem 2
x + -0.5 = -9.287087811 Simplifying x + -0.5 = -9.287087811 Reorder the terms: -0.5 + x = -9.287087811 Solving -0.5 + x = -9.287087811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -9.287087811 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -9.287087811 + 0.5 x = -9.287087811 + 0.5 Combine like terms: -9.287087811 + 0.5 = -8.787087811 x = -8.787087811 Simplifying x = -8.787087811Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.787087811, -8.787087811}
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