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Simplifying 6x8 + -24x7 + 12x6 = 0 Reorder the terms: 12x6 + -24x7 + 6x8 = 0 Solving 12x6 + -24x7 + 6x8 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x6'. 6x6(2 + -4x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'x6' equal to zero and attempt to solve: Simplifying x6 = 0 Solving x6 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x6 = 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 + -4x + x2)' equal to zero and attempt to solve: Simplifying 2 + -4x + x2 = 0 Solving 2 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + -4x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -4x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4x + x2 = 0 + -2 -4x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4x + x2 = -2 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -2 + 4 Reorder the terms: 4 + -4x + x2 = -2 + 4 Combine like terms: -2 + 4 = 2 4 + -4x + x2 = 2 Factor a perfect square on the left side: (x + -2)(x + -2) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -2) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -2 = 1.414213562 Simplifying x + -2 = 1.414213562 Reorder the terms: -2 + x = 1.414213562 Solving -2 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.414213562 + 2 x = 1.414213562 + 2 Combine like terms: 1.414213562 + 2 = 3.414213562 x = 3.414213562 Simplifying x = 3.414213562Subproblem 2
x + -2 = -1.414213562 Simplifying x + -2 = -1.414213562 Reorder the terms: -2 + x = -1.414213562 Solving -2 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.414213562 + 2 x = -1.414213562 + 2 Combine like terms: -1.414213562 + 2 = 0.585786438 x = 0.585786438 Simplifying x = 0.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.414213562, 0.585786438}Solution
x = {3.414213562, 0.585786438}
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