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Simplifying 134813540400.72x2 + -135452084500x + 638544099.24123 = 0 Reorder the terms: 638544099.24123 + -135452084500x + 134813540400.72x2 = 0 Solving 638544099.24123 + -135452084500x + 134813540400.72x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 134813540400.72 the coefficient of the squared term: Divide each side by '134813540400.72'. 0.004736498258 + -1.004736498x + x2 = 0 Move the constant term to the right: Add '-0.004736498258' to each side of the equation. 0.004736498258 + -1.004736498x + -0.004736498258 + x2 = 0 + -0.004736498258 Reorder the terms: 0.004736498258 + -0.004736498258 + -1.004736498x + x2 = 0 + -0.004736498258 Combine like terms: 0.004736498258 + -0.004736498258 = 0.000000000000 0.000000000000 + -1.004736498x + x2 = 0 + -0.004736498258 -1.004736498x + x2 = 0 + -0.004736498258 Combine like terms: 0 + -0.004736498258 = -0.004736498258 -1.004736498x + x2 = -0.004736498258 The x term is -1.004736498x. Take half its coefficient (-0.502368249). Square it (0.2523738576) and add it to both sides. Add '0.2523738576' to each side of the equation. -1.004736498x + 0.2523738576 + x2 = -0.004736498258 + 0.2523738576 Reorder the terms: 0.2523738576 + -1.004736498x + x2 = -0.004736498258 + 0.2523738576 Combine like terms: -0.004736498258 + 0.2523738576 = 0.247637359342 0.2523738576 + -1.004736498x + x2 = 0.247637359342 Factor a perfect square on the left side: (x + -0.502368249)(x + -0.502368249) = 0.247637359342 Calculate the square root of the right side: 0.497631751 Break this problem into two subproblems by setting (x + -0.502368249) equal to 0.497631751 and -0.497631751.Subproblem 1
x + -0.502368249 = 0.497631751 Simplifying x + -0.502368249 = 0.497631751 Reorder the terms: -0.502368249 + x = 0.497631751 Solving -0.502368249 + x = 0.497631751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.502368249' to each side of the equation. -0.502368249 + 0.502368249 + x = 0.497631751 + 0.502368249 Combine like terms: -0.502368249 + 0.502368249 = 0.000000000 0.000000000 + x = 0.497631751 + 0.502368249 x = 0.497631751 + 0.502368249 Combine like terms: 0.497631751 + 0.502368249 = 1 x = 1 Simplifying x = 1Subproblem 2
x + -0.502368249 = -0.497631751 Simplifying x + -0.502368249 = -0.497631751 Reorder the terms: -0.502368249 + x = -0.497631751 Solving -0.502368249 + x = -0.497631751 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.502368249' to each side of the equation. -0.502368249 + 0.502368249 + x = -0.497631751 + 0.502368249 Combine like terms: -0.502368249 + 0.502368249 = 0.000000000 0.000000000 + x = -0.497631751 + 0.502368249 x = -0.497631751 + 0.502368249 Combine like terms: -0.497631751 + 0.502368249 = 0.004736498 x = 0.004736498 Simplifying x = 0.004736498Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, 0.004736498}
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