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Simplifying 0 = 6x3 + -4x + -1x5 Reorder the terms: 0 = -4x + 6x3 + -1x5 Solving 0 = -4x + 6x3 + -1x5 Solving for variable 'x'. Remove the zero: 4x + -6x3 + x5 = -4x + 6x3 + -1x5 + 4x + -6x3 + x5 Reorder the terms: 4x + -6x3 + x5 = -4x + 4x + 6x3 + -6x3 + -1x5 + x5 Combine like terms: -4x + 4x = 0 4x + -6x3 + x5 = 0 + 6x3 + -6x3 + -1x5 + x5 4x + -6x3 + x5 = 6x3 + -6x3 + -1x5 + x5 Combine like terms: 6x3 + -6x3 = 0 4x + -6x3 + x5 = 0 + -1x5 + x5 4x + -6x3 + x5 = -1x5 + x5 Combine like terms: -1x5 + x5 = 0 4x + -6x3 + x5 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(4 + -6x2 + x4) = 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 '(4 + -6x2 + x4)' equal to zero and attempt to solve: Simplifying 4 + -6x2 + x4 = 0 Solving 4 + -6x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -6x2 + -4 + x4 = 0 + -4 Reorder the terms: 4 + -4 + -6x2 + x4 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -6x2 + x4 = 0 + -4 -6x2 + x4 = 0 + -4 Combine like terms: 0 + -4 = -4 -6x2 + x4 = -4 The x term is -6x2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x2 + 9 + x4 = -4 + 9 Reorder the terms: 9 + -6x2 + x4 = -4 + 9 Combine like terms: -4 + 9 = 5 9 + -6x2 + x4 = 5 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x2 + -3) equal to 2.236067978 and -2.236067978.Subproblem 1
x2 + -3 = 2.236067978 Simplifying x2 + -3 = 2.236067978 Reorder the terms: -3 + x2 = 2.236067978 Solving -3 + x2 = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 2.236067978 + 3 x2 = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 x2 = 5.236067978 Simplifying x2 = 5.236067978 Take the square root of each side: x = {-2.288245611, 2.288245611}Subproblem 2
x2 + -3 = -2.236067978 Simplifying x2 + -3 = -2.236067978 Reorder the terms: -3 + x2 = -2.236067978 Solving -3 + x2 = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -2.236067978 + 3 x2 = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 x2 = 0.763932022 Simplifying x2 = 0.763932022 Take the square root of each side: x = {-0.874032049, 0.874032049}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.288245611, 2.288245611, -0.874032049, 0.874032049}Solution
x = {0, -2.288245611, 2.288245611, -0.874032049, 0.874032049}
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