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Simplifying 2x2 + -2x4 + 1 = 0 Reorder the terms: 1 + 2x2 + -2x4 = 0 Solving 1 + 2x2 + -2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.5 + -1x2 + x4 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1x2 + 0.5 + x4 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1x2 + x4 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1x2 + x4 = 0 + 0.5 -1x2 + x4 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1x2 + x4 = 0.5 The x term is -1x2. 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. -1x2 + 0.25 + x4 = 0.5 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = 0.5 + 0.25 Combine like terms: 0.5 + 0.25 = 0.75 0.25 + -1x2 + x4 = 0.75 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 0.75 Calculate the square root of the right side: 0.866025404 Break this problem into two subproblems by setting (x2 + -0.5) equal to 0.866025404 and -0.866025404.Subproblem 1
x2 + -0.5 = 0.866025404 Simplifying x2 + -0.5 = 0.866025404 Reorder the terms: -0.5 + x2 = 0.866025404 Solving -0.5 + x2 = 0.866025404 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 = 0.866025404 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 0.866025404 + 0.5 x2 = 0.866025404 + 0.5 Combine like terms: 0.866025404 + 0.5 = 1.366025404 x2 = 1.366025404 Simplifying x2 = 1.366025404 Take the square root of each side: x = {-1.168770895, 1.168770895}Subproblem 2
x2 + -0.5 = -0.866025404 Simplifying x2 + -0.5 = -0.866025404 Reorder the terms: -0.5 + x2 = -0.866025404 Solving -0.5 + x2 = -0.866025404 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 = -0.866025404 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -0.866025404 + 0.5 x2 = -0.866025404 + 0.5 Combine like terms: -0.866025404 + 0.5 = -0.366025404 x2 = -0.366025404 Simplifying x2 = -0.366025404 Reorder the terms: 0.366025404 + x2 = -0.366025404 + 0.366025404 Combine like terms: -0.366025404 + 0.366025404 = 0.000000000 0.366025404 + 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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