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Simplifying 14x5 + 7x3 = 2x Reorder the terms: 7x3 + 14x5 = 2x Solving 7x3 + 14x5 = 2x Solving for variable 'x'. Reorder the terms: -2x + 7x3 + 14x5 = 2x + -2x Combine like terms: 2x + -2x = 0 -2x + 7x3 + 14x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-2 + 7x2 + 14x4) = 0Subproblem 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 '(-2 + 7x2 + 14x4)' equal to zero and attempt to solve: Simplifying -2 + 7x2 + 14x4 = 0 Solving -2 + 7x2 + 14x4 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.1428571429 + 0.5x2 + x4 = 0 Move the constant term to the right: Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.5x2 + 0.1428571429 + x4 = 0 + 0.1428571429 Reorder the terms: -0.1428571429 + 0.1428571429 + 0.5x2 + x4 = 0 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + 0.5x2 + x4 = 0 + 0.1428571429 0.5x2 + x4 = 0 + 0.1428571429 Combine like terms: 0 + 0.1428571429 = 0.1428571429 0.5x2 + x4 = 0.1428571429 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 = 0.1428571429 + 0.0625 Reorder the terms: 0.0625 + 0.5x2 + x4 = 0.1428571429 + 0.0625 Combine like terms: 0.1428571429 + 0.0625 = 0.2053571429 0.0625 + 0.5x2 + x4 = 0.2053571429 Factor a perfect square on the left side: (x2 + 0.25)(x2 + 0.25) = 0.2053571429 Calculate the square root of the right side: 0.453163484 Break this problem into two subproblems by setting (x2 + 0.25) equal to 0.453163484 and -0.453163484.Subproblem 1
x2 + 0.25 = 0.453163484 Simplifying x2 + 0.25 = 0.453163484 Reorder the terms: 0.25 + x2 = 0.453163484 Solving 0.25 + x2 = 0.453163484 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 = 0.453163484 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x2 = 0.453163484 + -0.25 x2 = 0.453163484 + -0.25 Combine like terms: 0.453163484 + -0.25 = 0.203163484 x2 = 0.203163484 Simplifying x2 = 0.203163484 Take the square root of each side: x = {-0.450736602, 0.450736602}Subproblem 2
x2 + 0.25 = -0.453163484 Simplifying x2 + 0.25 = -0.453163484 Reorder the terms: 0.25 + x2 = -0.453163484 Solving 0.25 + x2 = -0.453163484 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 = -0.453163484 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x2 = -0.453163484 + -0.25 x2 = -0.453163484 + -0.25 Combine like terms: -0.453163484 + -0.25 = -0.703163484 x2 = -0.703163484 Simplifying x2 = -0.703163484 Reorder the terms: 0.703163484 + x2 = -0.703163484 + 0.703163484 Combine like terms: -0.703163484 + 0.703163484 = 0.000000000 0.703163484 + 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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