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Simplifying x100 + -2x51 = x2 Reorder the terms: -2x51 + x100 = x2 Solving -2x51 + x100 = x2 Solving for variable 'x'. Reorder the terms: -1x2 + -2x51 + x100 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1x2 + -2x51 + x100 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-1 + -2x49 + x98) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-1 + -2x49 + x98)' equal to zero and attempt to solve: Simplifying -1 + -2x49 + x98 = 0 Solving -1 + -2x49 + x98 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -2x49 + 1 + x98 = 0 + 1 Reorder the terms: -1 + 1 + -2x49 + x98 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x49 + x98 = 0 + 1 -2x49 + x98 = 0 + 1 Combine like terms: 0 + 1 = 1 -2x49 + x98 = 1 The x term is -2x49. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x49 + 1 + x98 = 1 + 1 Reorder the terms: 1 + -2x49 + x98 = 1 + 1 Combine like terms: 1 + 1 = 2 1 + -2x49 + x98 = 2 Factor a perfect square on the left side: (x49 + -1)(x49 + -1) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x49 + -1) equal to 1.414213562 and -1.414213562.Subproblem 1
x49 + -1 = 1.414213562 Simplifying x49 + -1 = 1.414213562 Reorder the terms: -1 + x49 = 1.414213562 Solving -1 + x49 = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x49 = 1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + x49 = 1.414213562 + 1 x49 = 1.414213562 + 1 Combine like terms: 1.414213562 + 1 = 2.414213562 x49 = 2.414213562 Simplifying x49 = 2.414213562 Reorder the terms: -2.414213562 + x49 = 2.414213562 + -2.414213562 Combine like terms: 2.414213562 + -2.414213562 = 0.000000000 -2.414213562 + x49 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x49 + -1 = -1.414213562 Simplifying x49 + -1 = -1.414213562 Reorder the terms: -1 + x49 = -1.414213562 Solving -1 + x49 = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x49 = -1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + x49 = -1.414213562 + 1 x49 = -1.414213562 + 1 Combine like terms: -1.414213562 + 1 = -0.414213562 x49 = -0.414213562 Simplifying x49 = -0.414213562 Reorder the terms: 0.414213562 + x49 = -0.414213562 + 0.414213562 Combine like terms: -0.414213562 + 0.414213562 = 0.000000000 0.414213562 + x49 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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