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Simplifying 3x12 + 20x6 + 6 = 0 Reorder the terms: 6 + 20x6 + 3x12 = 0 Solving 6 + 20x6 + 3x12 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2 + 6.666666667x6 + x12 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 6.666666667x6 + -2 + x12 = 0 + -2 Reorder the terms: 2 + -2 + 6.666666667x6 + x12 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 6.666666667x6 + x12 = 0 + -2 6.666666667x6 + x12 = 0 + -2 Combine like terms: 0 + -2 = -2 6.666666667x6 + x12 = -2 The x term is 6.666666667x6. Take half its coefficient (3.333333334). Square it (11.11111112) and add it to both sides. Add '11.11111112' to each side of the equation. 6.666666667x6 + 11.11111112 + x12 = -2 + 11.11111112 Reorder the terms: 11.11111112 + 6.666666667x6 + x12 = -2 + 11.11111112 Combine like terms: -2 + 11.11111112 = 9.11111112 11.11111112 + 6.666666667x6 + x12 = 9.11111112 Factor a perfect square on the left side: (x6 + 3.333333334)(x6 + 3.333333334) = 9.11111112 Calculate the square root of the right side: 3.018461714 Break this problem into two subproblems by setting (x6 + 3.333333334) equal to 3.018461714 and -3.018461714.Subproblem 1
x6 + 3.333333334 = 3.018461714 Simplifying x6 + 3.333333334 = 3.018461714 Reorder the terms: 3.333333334 + x6 = 3.018461714 Solving 3.333333334 + x6 = 3.018461714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x6 = 3.018461714 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x6 = 3.018461714 + -3.333333334 x6 = 3.018461714 + -3.333333334 Combine like terms: 3.018461714 + -3.333333334 = -0.31487162 x6 = -0.31487162 Simplifying x6 = -0.31487162 Reorder the terms: 0.31487162 + x6 = -0.31487162 + 0.31487162 Combine like terms: -0.31487162 + 0.31487162 = 0.00000000 0.31487162 + x6 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x6 + 3.333333334 = -3.018461714 Simplifying x6 + 3.333333334 = -3.018461714 Reorder the terms: 3.333333334 + x6 = -3.018461714 Solving 3.333333334 + x6 = -3.018461714 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.333333334' to each side of the equation. 3.333333334 + -3.333333334 + x6 = -3.018461714 + -3.333333334 Combine like terms: 3.333333334 + -3.333333334 = 0.000000000 0.000000000 + x6 = -3.018461714 + -3.333333334 x6 = -3.018461714 + -3.333333334 Combine like terms: -3.018461714 + -3.333333334 = -6.351795048 x6 = -6.351795048 Simplifying x6 = -6.351795048 Reorder the terms: 6.351795048 + x6 = -6.351795048 + 6.351795048 Combine like terms: -6.351795048 + 6.351795048 = 0.000000000 6.351795048 + x6 = 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.
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