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Simplifying x2 + -1x + -9180 = 0 Reorder the terms: -9180 + -1x + x2 = 0 Solving -9180 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9180' to each side of the equation. -9180 + -1x + 9180 + x2 = 0 + 9180 Reorder the terms: -9180 + 9180 + -1x + x2 = 0 + 9180 Combine like terms: -9180 + 9180 = 0 0 + -1x + x2 = 0 + 9180 -1x + x2 = 0 + 9180 Combine like terms: 0 + 9180 = 9180 -1x + x2 = 9180 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 = 9180 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 9180 + 0.25 Combine like terms: 9180 + 0.25 = 9180.25 0.25 + -1x + x2 = 9180.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 9180.25 Calculate the square root of the right side: 95.813621161 Break this problem into two subproblems by setting (x + -0.5) equal to 95.813621161 and -95.813621161.Subproblem 1
x + -0.5 = 95.813621161 Simplifying x + -0.5 = 95.813621161 Reorder the terms: -0.5 + x = 95.813621161 Solving -0.5 + x = 95.813621161 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 = 95.813621161 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 95.813621161 + 0.5 x = 95.813621161 + 0.5 Combine like terms: 95.813621161 + 0.5 = 96.313621161 x = 96.313621161 Simplifying x = 96.313621161Subproblem 2
x + -0.5 = -95.813621161 Simplifying x + -0.5 = -95.813621161 Reorder the terms: -0.5 + x = -95.813621161 Solving -0.5 + x = -95.813621161 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 = -95.813621161 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -95.813621161 + 0.5 x = -95.813621161 + 0.5 Combine like terms: -95.813621161 + 0.5 = -95.313621161 x = -95.313621161 Simplifying x = -95.313621161Solution
The solution to the problem is based on the solutions from the subproblems. x = {96.313621161, -95.313621161}
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