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Simplifying 6x6 + -36x5 + 42x4 = 0 Reorder the terms: 42x4 + -36x5 + 6x6 = 0 Solving 42x4 + -36x5 + 6x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x4'. 6x4(7 + -6x + x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve: Simplifying x4 = 0 Solving x4 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x4 = 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 '(7 + -6x + x2)' equal to zero and attempt to solve: Simplifying 7 + -6x + x2 = 0 Solving 7 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -6x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -6x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6x + x2 = 0 + -7 -6x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6x + x2 = -7 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -7 + 9 Reorder the terms: 9 + -6x + x2 = -7 + 9 Combine like terms: -7 + 9 = 2 9 + -6x + x2 = 2 Factor a perfect square on the left side: (x + -3)(x + -3) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + -3) equal to 1.414213562 and -1.414213562.Subproblem 1
x + -3 = 1.414213562 Simplifying x + -3 = 1.414213562 Reorder the terms: -3 + x = 1.414213562 Solving -3 + x = 1.414213562 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 + x = 1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + x = 1.414213562 + 3 x = 1.414213562 + 3 Combine like terms: 1.414213562 + 3 = 4.414213562 x = 4.414213562 Simplifying x = 4.414213562Subproblem 2
x + -3 = -1.414213562 Simplifying x + -3 = -1.414213562 Reorder the terms: -3 + x = -1.414213562 Solving -3 + x = -1.414213562 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 + x = -1.414213562 + 3 Combine like terms: -3 + 3 = 0 0 + x = -1.414213562 + 3 x = -1.414213562 + 3 Combine like terms: -1.414213562 + 3 = 1.585786438 x = 1.585786438 Simplifying x = 1.585786438Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.414213562, 1.585786438}Solution
x = {4.414213562, 1.585786438}
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