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Simplifying 12x6 + -10x3 + -5 = 0 Reorder the terms: -5 + -10x3 + 12x6 = 0 Solving -5 + -10x3 + 12x6 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.4166666667 + -0.8333333333x3 + x6 = 0 Move the constant term to the right: Add '0.4166666667' to each side of the equation. -0.4166666667 + -0.8333333333x3 + 0.4166666667 + x6 = 0 + 0.4166666667 Reorder the terms: -0.4166666667 + 0.4166666667 + -0.8333333333x3 + x6 = 0 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + -0.8333333333x3 + x6 = 0 + 0.4166666667 -0.8333333333x3 + x6 = 0 + 0.4166666667 Combine like terms: 0 + 0.4166666667 = 0.4166666667 -0.8333333333x3 + x6 = 0.4166666667 The x term is -0.8333333333x3. Take half its coefficient (-0.4166666667). Square it (0.1736111111) and add it to both sides. Add '0.1736111111' to each side of the equation. -0.8333333333x3 + 0.1736111111 + x6 = 0.4166666667 + 0.1736111111 Reorder the terms: 0.1736111111 + -0.8333333333x3 + x6 = 0.4166666667 + 0.1736111111 Combine like terms: 0.4166666667 + 0.1736111111 = 0.5902777778 0.1736111111 + -0.8333333333x3 + x6 = 0.5902777778 Factor a perfect square on the left side: (x3 + -0.4166666667)(x3 + -0.4166666667) = 0.5902777778 Calculate the square root of the right side: 0.768295371 Break this problem into two subproblems by setting (x3 + -0.4166666667) equal to 0.768295371 and -0.768295371.Subproblem 1
x3 + -0.4166666667 = 0.768295371 Simplifying x3 + -0.4166666667 = 0.768295371 Reorder the terms: -0.4166666667 + x3 = 0.768295371 Solving -0.4166666667 + x3 = 0.768295371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x3 = 0.768295371 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x3 = 0.768295371 + 0.4166666667 x3 = 0.768295371 + 0.4166666667 Combine like terms: 0.768295371 + 0.4166666667 = 1.1849620377 x3 = 1.1849620377 Simplifying x3 = 1.1849620377 Reorder the terms: -1.1849620377 + x3 = 1.1849620377 + -1.1849620377 Combine like terms: 1.1849620377 + -1.1849620377 = 0.0000000000 -1.1849620377 + 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 + -0.4166666667 = -0.768295371 Simplifying x3 + -0.4166666667 = -0.768295371 Reorder the terms: -0.4166666667 + x3 = -0.768295371 Solving -0.4166666667 + x3 = -0.768295371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4166666667' to each side of the equation. -0.4166666667 + 0.4166666667 + x3 = -0.768295371 + 0.4166666667 Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000 0.0000000000 + x3 = -0.768295371 + 0.4166666667 x3 = -0.768295371 + 0.4166666667 Combine like terms: -0.768295371 + 0.4166666667 = -0.3516287043 x3 = -0.3516287043 Simplifying x3 = -0.3516287043 Reorder the terms: 0.3516287043 + x3 = -0.3516287043 + 0.3516287043 Combine like terms: -0.3516287043 + 0.3516287043 = 0.0000000000 0.3516287043 + 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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