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Simplifying 6x4 + 12x2 = 126 Reorder the terms: 12x2 + 6x4 = 126 Solving 12x2 + 6x4 = 126 Solving for variable 'x'. Reorder the terms: -126 + 12x2 + 6x4 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + 12x2 + 6x4 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-21 + 2x2 + x4) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-21 + 2x2 + x4)' equal to zero and attempt to solve: Simplifying -21 + 2x2 + x4 = 0 Solving -21 + 2x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 2x2 + 21 + x4 = 0 + 21 Reorder the terms: -21 + 21 + 2x2 + x4 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 2x2 + x4 = 0 + 21 2x2 + x4 = 0 + 21 Combine like terms: 0 + 21 = 21 2x2 + x4 = 21 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 = 21 + 1 Reorder the terms: 1 + 2x2 + x4 = 21 + 1 Combine like terms: 21 + 1 = 22 1 + 2x2 + x4 = 22 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (x2 + 1) equal to 4.69041576 and -4.69041576.Subproblem 1
x2 + 1 = 4.69041576 Simplifying x2 + 1 = 4.69041576 Reorder the terms: 1 + x2 = 4.69041576 Solving 1 + x2 = 4.69041576 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 = 4.69041576 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 4.69041576 + -1 x2 = 4.69041576 + -1 Combine like terms: 4.69041576 + -1 = 3.69041576 x2 = 3.69041576 Simplifying x2 = 3.69041576 Take the square root of each side: x = {-1.921045486, 1.921045486}Subproblem 2
x2 + 1 = -4.69041576 Simplifying x2 + 1 = -4.69041576 Reorder the terms: 1 + x2 = -4.69041576 Solving 1 + x2 = -4.69041576 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 = -4.69041576 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -4.69041576 + -1 x2 = -4.69041576 + -1 Combine like terms: -4.69041576 + -1 = -5.69041576 x2 = -5.69041576 Simplifying x2 = -5.69041576 Reorder the terms: 5.69041576 + x2 = -5.69041576 + 5.69041576 Combine like terms: -5.69041576 + 5.69041576 = 0.00000000 5.69041576 + x2 = 0.00000000 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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