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Simplifying 6x4 + 12x2 = 120 Reorder the terms: 12x2 + 6x4 = 120 Solving 12x2 + 6x4 = 120 Solving for variable 'x'. Reorder the terms: -120 + 12x2 + 6x4 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 12x2 + 6x4 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-20 + 2x2 + x4) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-20 + 2x2 + x4)' equal to zero and attempt to solve: Simplifying -20 + 2x2 + x4 = 0 Solving -20 + 2x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 2x2 + 20 + x4 = 0 + 20 Reorder the terms: -20 + 20 + 2x2 + x4 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 2x2 + x4 = 0 + 20 2x2 + x4 = 0 + 20 Combine like terms: 0 + 20 = 20 2x2 + x4 = 20 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = 20 + 1 Reorder the terms: 1 + 2x2 + x4 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + 2x2 + x4 = 21 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x2 + 1) equal to 4.582575695 and -4.582575695.Subproblem 1
x2 + 1 = 4.582575695 Simplifying x2 + 1 = 4.582575695 Reorder the terms: 1 + x2 = 4.582575695 Solving 1 + x2 = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 4.582575695 + -1 x2 = 4.582575695 + -1 Combine like terms: 4.582575695 + -1 = 3.582575695 x2 = 3.582575695 Simplifying x2 = 3.582575695 Take the square root of each side: x = {-1.892769319, 1.892769319}Subproblem 2
x2 + 1 = -4.582575695 Simplifying x2 + 1 = -4.582575695 Reorder the terms: 1 + x2 = -4.582575695 Solving 1 + x2 = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -4.582575695 + -1 x2 = -4.582575695 + -1 Combine like terms: -4.582575695 + -1 = -5.582575695 x2 = -5.582575695 Simplifying x2 = -5.582575695 Reorder the terms: 5.582575695 + x2 = -5.582575695 + 5.582575695 Combine like terms: -5.582575695 + 5.582575695 = 0.000000000 5.582575695 + 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. The solution to this equation could not be determined.
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