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Simplifying 0 = 18x3 + 4x2 + 14x Reorder the terms: 0 = 14x + 4x2 + 18x3 Solving 0 = 14x + 4x2 + 18x3 Solving for variable 'x'. Remove the zero: -14x + -4x2 + -18x3 = 14x + 4x2 + 18x3 + -14x + -4x2 + -18x3 Reorder the terms: -14x + -4x2 + -18x3 = 14x + -14x + 4x2 + -4x2 + 18x3 + -18x3 Combine like terms: 14x + -14x = 0 -14x + -4x2 + -18x3 = 0 + 4x2 + -4x2 + 18x3 + -18x3 -14x + -4x2 + -18x3 = 4x2 + -4x2 + 18x3 + -18x3 Combine like terms: 4x2 + -4x2 = 0 -14x + -4x2 + -18x3 = 0 + 18x3 + -18x3 -14x + -4x2 + -18x3 = 18x3 + -18x3 Combine like terms: 18x3 + -18x3 = 0 -14x + -4x2 + -18x3 = 0 Factor out the Greatest Common Factor (GCF), '-2x'. -2x(7 + 2x + 9x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(7 + 2x + 9x2)' equal to zero and attempt to solve: Simplifying 7 + 2x + 9x2 = 0 Solving 7 + 2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.7777777778 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + 0.2222222222x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + 0.2222222222x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + 0.2222222222x + x2 = 0 + -0.7777777778 0.2222222222x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 0.2222222222x + x2 = -0.7777777778 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = -0.7777777778 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = -0.7777777778 + 0.01234567901 Combine like terms: -0.7777777778 + 0.01234567901 = -0.76543209879 0.01234567901 + 0.2222222222x + x2 = -0.76543209879 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = -0.76543209879 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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