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Simplifying x4 + x2 + -13 = 0 Reorder the terms: -13 + x2 + x4 = 0 Solving -13 + x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + x2 + 13 + x4 = 0 + 13 Reorder the terms: -13 + 13 + x2 + x4 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + x2 + x4 = 0 + 13 x2 + x4 = 0 + 13 Combine like terms: 0 + 13 = 13 x2 + x4 = 13 The x term is x2. 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. x2 + 0.25 + x4 = 13 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 13 + 0.25 Combine like terms: 13 + 0.25 = 13.25 0.25 + x2 + x4 = 13.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 13.25 Calculate the square root of the right side: 3.640054945 Break this problem into two subproblems by setting (x2 + 0.5) equal to 3.640054945 and -3.640054945.Subproblem 1
x2 + 0.5 = 3.640054945 Simplifying x2 + 0.5 = 3.640054945 Reorder the terms: 0.5 + x2 = 3.640054945 Solving 0.5 + x2 = 3.640054945 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 + x2 = 3.640054945 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 3.640054945 + -0.5 x2 = 3.640054945 + -0.5 Combine like terms: 3.640054945 + -0.5 = 3.140054945 x2 = 3.140054945 Simplifying x2 = 3.140054945 Take the square root of each side: x = {-1.772020018, 1.772020018}Subproblem 2
x2 + 0.5 = -3.640054945 Simplifying x2 + 0.5 = -3.640054945 Reorder the terms: 0.5 + x2 = -3.640054945 Solving 0.5 + x2 = -3.640054945 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 + x2 = -3.640054945 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -3.640054945 + -0.5 x2 = -3.640054945 + -0.5 Combine like terms: -3.640054945 + -0.5 = -4.140054945 x2 = -4.140054945 Simplifying x2 = -4.140054945 Reorder the terms: 4.140054945 + x2 = -4.140054945 + 4.140054945 Combine like terms: -4.140054945 + 4.140054945 = 0.000000000 4.140054945 + x2 = 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.
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