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Simplifying 14x6 + 6x3 + -12 = 0 Reorder the terms: -12 + 6x3 + 14x6 = 0 Solving -12 + 6x3 + 14x6 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 3x3 + 7x6) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 3x3 + 7x6)' equal to zero and attempt to solve: Simplifying -6 + 3x3 + 7x6 = 0 Solving -6 + 3x3 + 7x6 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + 0.4285714286x3 + x6 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 0.4285714286x3 + 0.8571428571 + x6 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 0.4285714286x3 + x6 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 0.4285714286x3 + x6 = 0 + 0.8571428571 0.4285714286x3 + x6 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 0.4285714286x3 + x6 = 0.8571428571 The x term is 0.4285714286x3. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286x3 + 0.04591836735 + x6 = 0.8571428571 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286x3 + x6 = 0.8571428571 + 0.04591836735 Combine like terms: 0.8571428571 + 0.04591836735 = 0.90306122445 0.04591836735 + 0.4285714286x3 + x6 = 0.90306122445 Factor a perfect square on the left side: (x3 + 0.2142857143)(x3 + 0.2142857143) = 0.90306122445 Calculate the square root of the right side: 0.950295335 Break this problem into two subproblems by setting (x3 + 0.2142857143) equal to 0.950295335 and -0.950295335.Subproblem 1
x3 + 0.2142857143 = 0.950295335 Simplifying x3 + 0.2142857143 = 0.950295335 Reorder the terms: 0.2142857143 + x3 = 0.950295335 Solving 0.2142857143 + x3 = 0.950295335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x3 = 0.950295335 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x3 = 0.950295335 + -0.2142857143 x3 = 0.950295335 + -0.2142857143 Combine like terms: 0.950295335 + -0.2142857143 = 0.7360096207 x3 = 0.7360096207 Simplifying x3 = 0.7360096207 Reorder the terms: -0.7360096207 + x3 = 0.7360096207 + -0.7360096207 Combine like terms: 0.7360096207 + -0.7360096207 = 0.0000000000 -0.7360096207 + 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 + 0.2142857143 = -0.950295335 Simplifying x3 + 0.2142857143 = -0.950295335 Reorder the terms: 0.2142857143 + x3 = -0.950295335 Solving 0.2142857143 + x3 = -0.950295335 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + x3 = -0.950295335 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + x3 = -0.950295335 + -0.2142857143 x3 = -0.950295335 + -0.2142857143 Combine like terms: -0.950295335 + -0.2142857143 = -1.1645810493 x3 = -1.1645810493 Simplifying x3 = -1.1645810493 Reorder the terms: 1.1645810493 + x3 = -1.1645810493 + 1.1645810493 Combine like terms: -1.1645810493 + 1.1645810493 = 0.0000000000 1.1645810493 + 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. 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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