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Simplifying 6x3 + -18x7 + -9x5 = 0 Reorder the terms: 6x3 + -9x5 + -18x7 = 0 Solving 6x3 + -9x5 + -18x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x3'. 3x3(2 + -3x2 + -6x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2 + -3x2 + -6x4)' equal to zero and attempt to solve: Simplifying 2 + -3x2 + -6x4 = 0 Solving 2 + -3x2 + -6x4 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.3333333333 + 0.5x2 + x4 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 0.5x2 + 0.3333333333 + x4 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 0.5x2 + x4 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 0.5x2 + x4 = 0 + 0.3333333333 0.5x2 + x4 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 0.5x2 + x4 = 0.3333333333 The x term is 0.5x2. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x2 + 0.0625 + x4 = 0.3333333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x2 + x4 = 0.3333333333 + 0.0625 Combine like terms: 0.3333333333 + 0.0625 = 0.3958333333 0.0625 + 0.5x2 + x4 = 0.3958333333 Factor a perfect square on the left side: (x2 + 0.25)(x2 + 0.25) = 0.3958333333 Calculate the square root of the right side: 0.62915287 Break this problem into two subproblems by setting (x2 + 0.25) equal to 0.62915287 and -0.62915287.Subproblem 1
x2 + 0.25 = 0.62915287 Simplifying x2 + 0.25 = 0.62915287 Reorder the terms: 0.25 + x2 = 0.62915287 Solving 0.25 + x2 = 0.62915287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x2 = 0.62915287 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x2 = 0.62915287 + -0.25 x2 = 0.62915287 + -0.25 Combine like terms: 0.62915287 + -0.25 = 0.37915287 x2 = 0.37915287 Simplifying x2 = 0.37915287 Take the square root of each side: x = {-0.615753904, 0.615753904}Subproblem 2
x2 + 0.25 = -0.62915287 Simplifying x2 + 0.25 = -0.62915287 Reorder the terms: 0.25 + x2 = -0.62915287 Solving 0.25 + x2 = -0.62915287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x2 = -0.62915287 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x2 = -0.62915287 + -0.25 x2 = -0.62915287 + -0.25 Combine like terms: -0.62915287 + -0.25 = -0.87915287 x2 = -0.87915287 Simplifying x2 = -0.87915287 Reorder the terms: 0.87915287 + x2 = -0.87915287 + 0.87915287 Combine like terms: -0.87915287 + 0.87915287 = 0.00000000 0.87915287 + x2 = 0.00000000 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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