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Simplifying -4428x + 1300x3 + -126x5 + 4x7 + -4x(x2 + -9)(x4 + -27x2) = 0 Reorder the terms: -4428x + 1300x3 + -126x5 + 4x7 + -4x(-9 + x2)(x4 + -27x2) = 0 Reorder the terms: -4428x + 1300x3 + -126x5 + 4x7 + -4x(-9 + x2)(-27x2 + x4) = 0 Multiply (-9 + x2) * (-27x2 + x4) -4428x + 1300x3 + -126x5 + 4x7 + -4x(-9(-27x2 + x4) + x2(-27x2 + x4)) = 0 -4428x + 1300x3 + -126x5 + 4x7 + -4x((-27x2 * -9 + x4 * -9) + x2(-27x2 + x4)) = 0 -4428x + 1300x3 + -126x5 + 4x7 + -4x((243x2 + -9x4) + x2(-27x2 + x4)) = 0 -4428x + 1300x3 + -126x5 + 4x7 + -4x(243x2 + -9x4 + (-27x2 * x2 + x4 * x2)) = 0 -4428x + 1300x3 + -126x5 + 4x7 + -4x(243x2 + -9x4 + (-27x4 + x6)) = 0 Combine like terms: -9x4 + -27x4 = -36x4 -4428x + 1300x3 + -126x5 + 4x7 + -4x(243x2 + -36x4 + x6) = 0 -4428x + 1300x3 + -126x5 + 4x7 + (243x2 * -4x + -36x4 * -4x + x6 * -4x) = 0 -4428x + 1300x3 + -126x5 + 4x7 + (-972x3 + 144x5 + -4x7) = 0 Reorder the terms: -4428x + 1300x3 + -972x3 + -126x5 + 144x5 + 4x7 + -4x7 = 0 Combine like terms: 1300x3 + -972x3 = 328x3 -4428x + 328x3 + -126x5 + 144x5 + 4x7 + -4x7 = 0 Combine like terms: -126x5 + 144x5 = 18x5 -4428x + 328x3 + 18x5 + 4x7 + -4x7 = 0 Combine like terms: 4x7 + -4x7 = 0 -4428x + 328x3 + 18x5 + 0 = 0 -4428x + 328x3 + 18x5 = 0 Solving -4428x + 328x3 + 18x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-2214 + 164x2 + 9x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-2214 + 164x2 + 9x4)' equal to zero and attempt to solve: Simplifying -2214 + 164x2 + 9x4 = 0 Solving -2214 + 164x2 + 9x4 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -246 + 18.22222222x2 + x4 = 0 Move the constant term to the right: Add '246' to each side of the equation. -246 + 18.22222222x2 + 246 + x4 = 0 + 246 Reorder the terms: -246 + 246 + 18.22222222x2 + x4 = 0 + 246 Combine like terms: -246 + 246 = 0 0 + 18.22222222x2 + x4 = 0 + 246 18.22222222x2 + x4 = 0 + 246 Combine like terms: 0 + 246 = 246 18.22222222x2 + x4 = 246 The x term is 18.22222222x2. Take half its coefficient (9.11111111). Square it (83.01234566) and add it to both sides. Add '83.01234566' to each side of the equation. 18.22222222x2 + 83.01234566 + x4 = 246 + 83.01234566 Reorder the terms: 83.01234566 + 18.22222222x2 + x4 = 246 + 83.01234566 Combine like terms: 246 + 83.01234566 = 329.01234566 83.01234566 + 18.22222222x2 + x4 = 329.01234566 Factor a perfect square on the left side: (x2 + 9.11111111)(x2 + 9.11111111) = 329.01234566 Calculate the square root of the right side: 18.138697463 Break this problem into two subproblems by setting (x2 + 9.11111111) equal to 18.138697463 and -18.138697463.Subproblem 1
x2 + 9.11111111 = 18.138697463 Simplifying x2 + 9.11111111 = 18.138697463 Reorder the terms: 9.11111111 + x2 = 18.138697463 Solving 9.11111111 + x2 = 18.138697463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.11111111' to each side of the equation. 9.11111111 + -9.11111111 + x2 = 18.138697463 + -9.11111111 Combine like terms: 9.11111111 + -9.11111111 = 0.00000000 0.00000000 + x2 = 18.138697463 + -9.11111111 x2 = 18.138697463 + -9.11111111 Combine like terms: 18.138697463 + -9.11111111 = 9.027586353 x2 = 9.027586353 Simplifying x2 = 9.027586353 Take the square root of each side: x = {-3.004594208, 3.004594208}Subproblem 2
x2 + 9.11111111 = -18.138697463 Simplifying x2 + 9.11111111 = -18.138697463 Reorder the terms: 9.11111111 + x2 = -18.138697463 Solving 9.11111111 + x2 = -18.138697463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.11111111' to each side of the equation. 9.11111111 + -9.11111111 + x2 = -18.138697463 + -9.11111111 Combine like terms: 9.11111111 + -9.11111111 = 0.00000000 0.00000000 + x2 = -18.138697463 + -9.11111111 x2 = -18.138697463 + -9.11111111 Combine like terms: -18.138697463 + -9.11111111 = -27.249808573 x2 = -27.249808573 Simplifying x2 = -27.249808573 Reorder the terms: 27.249808573 + x2 = -27.249808573 + 27.249808573 Combine like terms: -27.249808573 + 27.249808573 = 0.000000000 27.249808573 + 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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