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Simplifying x2 + x + 3 = 117 Reorder the terms: 3 + x + x2 = 117 Solving 3 + x + x2 = 117 Solving for variable 'x'. Reorder the terms: 3 + -117 + x + x2 = 117 + -117 Combine like terms: 3 + -117 = -114 -114 + x + x2 = 117 + -117 Combine like terms: 117 + -117 = 0 -114 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '114' to each side of the equation. -114 + x + 114 + x2 = 0 + 114 Reorder the terms: -114 + 114 + x + x2 = 0 + 114 Combine like terms: -114 + 114 = 0 0 + x + x2 = 0 + 114 x + x2 = 0 + 114 Combine like terms: 0 + 114 = 114 x + x2 = 114 The x term is x. 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. x + 0.25 + x2 = 114 + 0.25 Reorder the terms: 0.25 + x + x2 = 114 + 0.25 Combine like terms: 114 + 0.25 = 114.25 0.25 + x + 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 = 10.188779163 x = 10.188779163 Simplifying x = 10.188779163Subproblem 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 = -11.188779163 x = -11.188779163 Simplifying x = -11.188779163Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.188779163, -11.188779163}
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