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Simplifying x4 + 2012x2 + 2013 = 0 Reorder the terms: 2013 + 2012x2 + x4 = 0 Solving 2013 + 2012x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2013' to each side of the equation. 2013 + 2012x2 + -2013 + x4 = 0 + -2013 Reorder the terms: 2013 + -2013 + 2012x2 + x4 = 0 + -2013 Combine like terms: 2013 + -2013 = 0 0 + 2012x2 + x4 = 0 + -2013 2012x2 + x4 = 0 + -2013 Combine like terms: 0 + -2013 = -2013 2012x2 + x4 = -2013 The x term is 2012x2. Take half its coefficient (1006). Square it (1012036) and add it to both sides. Add '1012036' to each side of the equation. 2012x2 + 1012036 + x4 = -2013 + 1012036 Reorder the terms: 1012036 + 2012x2 + x4 = -2013 + 1012036 Combine like terms: -2013 + 1012036 = 1010023 1012036 + 2012x2 + x4 = 1010023 Factor a perfect square on the left side: (x2 + 1006)(x2 + 1006) = 1010023 Calculate the square root of the right side: 1004.999004975 Break this problem into two subproblems by setting (x2 + 1006) equal to 1004.999004975 and -1004.999004975.Subproblem 1
x2 + 1006 = 1004.999004975 Simplifying x2 + 1006 = 1004.999004975 Reorder the terms: 1006 + x2 = 1004.999004975 Solving 1006 + x2 = 1004.999004975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1006' to each side of the equation. 1006 + -1006 + x2 = 1004.999004975 + -1006 Combine like terms: 1006 + -1006 = 0 0 + x2 = 1004.999004975 + -1006 x2 = 1004.999004975 + -1006 Combine like terms: 1004.999004975 + -1006 = -1.000995025 x2 = -1.000995025 Simplifying x2 = -1.000995025 Reorder the terms: 1.000995025 + x2 = -1.000995025 + 1.000995025 Combine like terms: -1.000995025 + 1.000995025 = 0.000000000 1.000995025 + x2 = 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
x2 + 1006 = -1004.999004975 Simplifying x2 + 1006 = -1004.999004975 Reorder the terms: 1006 + x2 = -1004.999004975 Solving 1006 + x2 = -1004.999004975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1006' to each side of the equation. 1006 + -1006 + x2 = -1004.999004975 + -1006 Combine like terms: 1006 + -1006 = 0 0 + x2 = -1004.999004975 + -1006 x2 = -1004.999004975 + -1006 Combine like terms: -1004.999004975 + -1006 = -2010.999004975 x2 = -2010.999004975 Simplifying x2 = -2010.999004975 Reorder the terms: 2010.999004975 + x2 = -2010.999004975 + 2010.999004975 Combine like terms: -2010.999004975 + 2010.999004975 = 0.000000000 2010.999004975 + 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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