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Simplifying (18x3 + 14x2 + 10x) = 0 Reorder the terms: (10x + 14x2 + 18x3) = 0 Remove parenthesis around (10x + 14x2 + 18x3) 10x + 14x2 + 18x3 = 0 Solving 10x + 14x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(5 + 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 '(5 + 7x + 9x2)' equal to zero and attempt to solve: Simplifying 5 + 7x + 9x2 = 0 Solving 5 + 7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.5555555556 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + 0.7777777778x + -0.5555555556 + x2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + 0.7777777778x + x2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + 0.7777777778x + x2 = 0 + -0.5555555556 0.7777777778x + x2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 0.7777777778x + x2 = -0.5555555556 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 = -0.5555555556 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = -0.5555555556 + 0.1512345679 Combine like terms: -0.5555555556 + 0.1512345679 = -0.4043209877 0.1512345679 + 0.7777777778x + x2 = -0.4043209877 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = -0.4043209877 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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