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Simplifying x2 + -1x + -114 = 0 Reorder the terms: -114 + -1x + x2 = 0 Solving -114 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '114' to each side of the equation. -114 + -1x + 114 + x2 = 0 + 114 Reorder the terms: -114 + 114 + -1x + x2 = 0 + 114 Combine like terms: -114 + 114 = 0 0 + -1x + x2 = 0 + 114 -1x + x2 = 0 + 114 Combine like terms: 0 + 114 = 114 -1x + x2 = 114 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 = 114 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 114 + 0.25 Combine like terms: 114 + 0.25 = 114.25 0.25 + -1x + x2 = 114.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 114.25 Calculate the square root of the right side: 10.688779163 Break this problem into two subproblems by setting (x + -0.5) equal to 10.688779163 and -10.688779163.Subproblem 1
x + -0.5 = 10.688779163 Simplifying x + -0.5 = 10.688779163 Reorder the terms: -0.5 + x = 10.688779163 Solving -0.5 + x = 10.688779163 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 = 10.688779163 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 10.688779163 + 0.5 x = 10.688779163 + 0.5 Combine like terms: 10.688779163 + 0.5 = 11.188779163 x = 11.188779163 Simplifying x = 11.188779163Subproblem 2
x + -0.5 = -10.688779163 Simplifying x + -0.5 = -10.688779163 Reorder the terms: -0.5 + x = -10.688779163 Solving -0.5 + x = -10.688779163 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 = -10.688779163 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -10.688779163 + 0.5 x = -10.688779163 + 0.5 Combine like terms: -10.688779163 + 0.5 = -10.188779163 x = -10.188779163 Simplifying x = -10.188779163Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.188779163, -10.188779163}
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