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Simplifying x4 + x2 = 0.0036 Reorder the terms: x2 + x4 = 0.0036 Solving x2 + x4 = 0.0036 Solving for variable 'x'. Reorder the terms: -0.0036 + x2 + x4 = 0.0036 + -0.0036 Combine like terms: 0.0036 + -0.0036 = 0.0000 -0.0036 + x2 + x4 = 0.0000 Begin completing the square. Move the constant term to the right: Add '0.0036' to each side of the equation. -0.0036 + x2 + 0.0036 + x4 = 0.0000 + 0.0036 Reorder the terms: -0.0036 + 0.0036 + x2 + x4 = 0.0000 + 0.0036 Combine like terms: -0.0036 + 0.0036 = 0.0000 0.0000 + x2 + x4 = 0.0000 + 0.0036 x2 + x4 = 0.0000 + 0.0036 Combine like terms: 0.0000 + 0.0036 = 0.0036 x2 + x4 = 0.0036 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 = 0.0036 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 0.0036 + 0.25 Combine like terms: 0.0036 + 0.25 = 0.2536 0.25 + x2 + x4 = 0.2536 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 0.2536 Calculate the square root of the right side: 0.503587132 Break this problem into two subproblems by setting (x2 + 0.5) equal to 0.503587132 and -0.503587132.Subproblem 1
x2 + 0.5 = 0.503587132 Simplifying x2 + 0.5 = 0.503587132 Reorder the terms: 0.5 + x2 = 0.503587132 Solving 0.5 + x2 = 0.503587132 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 = 0.503587132 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 0.503587132 + -0.5 x2 = 0.503587132 + -0.5 Combine like terms: 0.503587132 + -0.5 = 0.003587132 x2 = 0.003587132 Simplifying x2 = 0.003587132 Take the square root of each side: x = {-0.059892671, 0.059892671}Subproblem 2
x2 + 0.5 = -0.503587132 Simplifying x2 + 0.5 = -0.503587132 Reorder the terms: 0.5 + x2 = -0.503587132 Solving 0.5 + x2 = -0.503587132 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 = -0.503587132 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -0.503587132 + -0.5 x2 = -0.503587132 + -0.5 Combine like terms: -0.503587132 + -0.5 = -1.003587132 x2 = -1.003587132 Simplifying x2 = -1.003587132 Reorder the terms: 1.003587132 + x2 = -1.003587132 + 1.003587132 Combine like terms: -1.003587132 + 1.003587132 = 0.000000000 1.003587132 + 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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