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Simplifying 3x4 + -4 + 2x2 + 5x4 = 0 Reorder the terms: -4 + 2x2 + 3x4 + 5x4 = 0 Combine like terms: 3x4 + 5x4 = 8x4 -4 + 2x2 + 8x4 = 0 Solving -4 + 2x2 + 8x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + x2 + 4x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + x2 + 4x4)' equal to zero and attempt to solve: Simplifying -2 + x2 + 4x4 = 0 Solving -2 + x2 + 4x4 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5 + 0.25x2 + x4 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 0.25x2 + 0.5 + x4 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 0.25x2 + x4 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 0.25x2 + x4 = 0 + 0.5 0.25x2 + x4 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 0.25x2 + x4 = 0.5 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. 0.25x2 + 0.25 + x4 = 0.5 + 0.25 Reorder the terms: 0.25 + 0.25x2 + x4 = 0.5 + 0.25 Combine like terms: 0.5 + 0.25 = 0.75 0.25 + 0.25x2 + 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 = 0.366025404 x2 = 0.366025404 Simplifying x2 = 0.366025404 Take the square root of each side: x = {-0.605000334, 0.605000334}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 = -1.366025404 x2 = -1.366025404 Simplifying x2 = -1.366025404 Reorder the terms: 1.366025404 + x2 = -1.366025404 + 1.366025404 Combine like terms: -1.366025404 + 1.366025404 = 0.000000000 1.366025404 + 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. 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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