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Simplifying 18x3 + -14x2 + 6x = 0 Reorder the terms: 6x + -14x2 + 18x3 = 0 Solving 6x + -14x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(3 + -7x + 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 '(3 + -7x + 9x2)' equal to zero and attempt to solve: Simplifying 3 + -7x + 9x2 = 0 Solving 3 + -7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.3333333333 + -0.7777777778x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -0.7777777778x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -0.7777777778x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -0.7777777778x + x2 = 0 + -0.3333333333 -0.7777777778x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -0.7777777778x + x2 = -0.3333333333 The x term is -0.7777777778x. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778x + 0.1512345679 + x2 = -0.3333333333 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778x + x2 = -0.3333333333 + 0.1512345679 Combine like terms: -0.3333333333 + 0.1512345679 = -0.1820987654 0.1512345679 + -0.7777777778x + x2 = -0.1820987654 Factor a perfect square on the left side: (x + -0.3888888889)(x + -0.3888888889) = -0.1820987654 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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