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Simplifying 6x6 + 7x3 + -8 = 0 Reorder the terms: -8 + 7x3 + 6x6 = 0 Solving -8 + 7x3 + 6x6 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.333333333 + 1.166666667x3 + x6 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 1.166666667x3 + 1.333333333 + x6 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 1.166666667x3 + x6 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 1.166666667x3 + x6 = 0 + 1.333333333 1.166666667x3 + x6 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 1.166666667x3 + x6 = 1.333333333 The x term is 1.166666667x3. Take half its coefficient (0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. 1.166666667x3 + 0.3402777780 + x6 = 1.333333333 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x3 + x6 = 1.333333333 + 0.3402777780 Combine like terms: 1.333333333 + 0.3402777780 = 1.673611111 0.3402777780 + 1.166666667x3 + x6 = 1.673611111 Factor a perfect square on the left side: (x3 + 0.5833333335)(x3 + 0.5833333335) = 1.673611111 Calculate the square root of the right side: 1.293681225 Break this problem into two subproblems by setting (x3 + 0.5833333335) equal to 1.293681225 and -1.293681225.Subproblem 1
x3 + 0.5833333335 = 1.293681225 Simplifying x3 + 0.5833333335 = 1.293681225 Reorder the terms: 0.5833333335 + x3 = 1.293681225 Solving 0.5833333335 + x3 = 1.293681225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x3 = 1.293681225 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x3 = 1.293681225 + -0.5833333335 x3 = 1.293681225 + -0.5833333335 Combine like terms: 1.293681225 + -0.5833333335 = 0.7103478915 x3 = 0.7103478915 Simplifying x3 = 0.7103478915 Reorder the terms: -0.7103478915 + x3 = 0.7103478915 + -0.7103478915 Combine like terms: 0.7103478915 + -0.7103478915 = 0.0000000000 -0.7103478915 + x3 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x3 + 0.5833333335 = -1.293681225 Simplifying x3 + 0.5833333335 = -1.293681225 Reorder the terms: 0.5833333335 + x3 = -1.293681225 Solving 0.5833333335 + x3 = -1.293681225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5833333335' to each side of the equation. 0.5833333335 + -0.5833333335 + x3 = -1.293681225 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x3 = -1.293681225 + -0.5833333335 x3 = -1.293681225 + -0.5833333335 Combine like terms: -1.293681225 + -0.5833333335 = -1.8770145585 x3 = -1.8770145585 Simplifying x3 = -1.8770145585 Reorder the terms: 1.8770145585 + x3 = -1.8770145585 + 1.8770145585 Combine like terms: -1.8770145585 + 1.8770145585 = 0.0000000000 1.8770145585 + x3 = 0.0000000000 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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