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Simplifying 2x6 + -2x4 + -14x2 = 0 Reorder the terms: -14x2 + -2x4 + 2x6 = 0 Solving -14x2 + -2x4 + 2x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x2'. 2x2(-7 + -1x2 + x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-7 + -1x2 + x4)' equal to zero and attempt to solve: Simplifying -7 + -1x2 + x4 = 0 Solving -7 + -1x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -1x2 + 7 + x4 = 0 + 7 Reorder the terms: -7 + 7 + -1x2 + x4 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x2 + x4 = 0 + 7 -1x2 + x4 = 0 + 7 Combine like terms: 0 + 7 = 7 -1x2 + x4 = 7 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 = 7 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = 7 + 0.25 Combine like terms: 7 + 0.25 = 7.25 0.25 + -1x2 + x4 = 7.25 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x2 + -0.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x2 + -0.5 = 2.692582404 Simplifying x2 + -0.5 = 2.692582404 Reorder the terms: -0.5 + x2 = 2.692582404 Solving -0.5 + x2 = 2.692582404 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 = 2.692582404 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 2.692582404 + 0.5 x2 = 2.692582404 + 0.5 Combine like terms: 2.692582404 + 0.5 = 3.192582404 x2 = 3.192582404 Simplifying x2 = 3.192582404 Take the square root of each side: x = {-1.786779898, 1.786779898}Subproblem 2
x2 + -0.5 = -2.692582404 Simplifying x2 + -0.5 = -2.692582404 Reorder the terms: -0.5 + x2 = -2.692582404 Solving -0.5 + x2 = -2.692582404 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 = -2.692582404 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -2.692582404 + 0.5 x2 = -2.692582404 + 0.5 Combine like terms: -2.692582404 + 0.5 = -2.192582404 x2 = -2.192582404 Simplifying x2 = -2.192582404 Reorder the terms: 2.192582404 + x2 = -2.192582404 + 2.192582404 Combine like terms: -2.192582404 + 2.192582404 = 0.000000000 2.192582404 + 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.Solution
x = {0}
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