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Simplifying (x2 + 0.2)(x2 + 0.2) = 0 Reorder the terms: (0.2 + x2)(x2 + 0.2) = 0 Reorder the terms: (0.2 + x2)(0.2 + x2) = 0 Multiply (0.2 + x2) * (0.2 + x2) (0.2(0.2 + x2) + x2(0.2 + x2)) = 0 ((0.2 * 0.2 + x2 * 0.2) + x2(0.2 + x2)) = 0 ((0.04 + 0.2x2) + x2(0.2 + x2)) = 0 (0.04 + 0.2x2 + (0.2 * x2 + x2 * x2)) = 0 (0.04 + 0.2x2 + (0.2x2 + x4)) = 0 Combine like terms: 0.2x2 + 0.2x2 = 0.4x2 (0.04 + 0.4x2 + x4) = 0 Solving 0.04 + 0.4x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.04' to each side of the equation. 0.04 + 0.4x2 + -0.04 + x4 = 0 + -0.04 Reorder the terms: 0.04 + -0.04 + 0.4x2 + x4 = 0 + -0.04 Combine like terms: 0.04 + -0.04 = 0.00 0.00 + 0.4x2 + x4 = 0 + -0.04 0.4x2 + x4 = 0 + -0.04 Combine like terms: 0 + -0.04 = -0.04 0.4x2 + x4 = -0.04 The x term is 0.4x2. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x2 + 0.04 + x4 = -0.04 + 0.04 Reorder the terms: 0.04 + 0.4x2 + x4 = -0.04 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.04 + 0.4x2 + x4 = 0.00 Factor a perfect square on the left side: (x2 + 0.2)(x2 + 0.2) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x2 + 0.2) equal to 0.00 and 0.00.Subproblem 1
x2 + 0.2 = 0.00 Simplifying x2 + 0.2 = 0.00 Reorder the terms: 0.2 + x2 = 0.00 Solving 0.2 + x2 = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x2 = 0.00 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x2 = 0.00 + -0.2 x2 = 0.00 + -0.2 Combine like terms: 0.00 + -0.2 = -0.2 x2 = -0.2 Simplifying x2 = -0.2 Reorder the terms: 0.2 + x2 = -0.2 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.2 + x2 = 0.0 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 0.2 = 0.00 Simplifying x2 + 0.2 = 0.00 Reorder the terms: 0.2 + x2 = 0.00 Solving 0.2 + x2 = 0.00 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x2 = 0.00 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x2 = 0.00 + -0.2 x2 = 0.00 + -0.2 Combine like terms: 0.00 + -0.2 = -0.2 x2 = -0.2 Simplifying x2 = -0.2 Reorder the terms: 0.2 + x2 = -0.2 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.2 + x2 = 0.0 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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