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Simplifying 18x3 + -5x2 + -9x = 0 Reorder the terms: -9x + -5x2 + 18x3 = 0 Solving -9x + -5x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-9 + -5x + 18x2) = 0Subproblem 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 '(-9 + -5x + 18x2)' equal to zero and attempt to solve: Simplifying -9 + -5x + 18x2 = 0 Solving -9 + -5x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -0.5 + -0.2777777778x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.2777777778x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.2777777778x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.2777777778x + x2 = 0 + 0.5 -0.2777777778x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.2777777778x + x2 = 0.5 The x term is -0.2777777778x. Take half its coefficient (-0.1388888889). Square it (0.01929012346) and add it to both sides. Add '0.01929012346' to each side of the equation. -0.2777777778x + 0.01929012346 + x2 = 0.5 + 0.01929012346 Reorder the terms: 0.01929012346 + -0.2777777778x + x2 = 0.5 + 0.01929012346 Combine like terms: 0.5 + 0.01929012346 = 0.51929012346 0.01929012346 + -0.2777777778x + x2 = 0.51929012346 Factor a perfect square on the left side: (x + -0.1388888889)(x + -0.1388888889) = 0.51929012346 Calculate the square root of the right side: 0.720617876 Break this problem into two subproblems by setting (x + -0.1388888889) equal to 0.720617876 and -0.720617876.Subproblem 1
x + -0.1388888889 = 0.720617876 Simplifying x + -0.1388888889 = 0.720617876 Reorder the terms: -0.1388888889 + x = 0.720617876 Solving -0.1388888889 + x = 0.720617876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1388888889' to each side of the equation. -0.1388888889 + 0.1388888889 + x = 0.720617876 + 0.1388888889 Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000 0.0000000000 + x = 0.720617876 + 0.1388888889 x = 0.720617876 + 0.1388888889 Combine like terms: 0.720617876 + 0.1388888889 = 0.8595067649 x = 0.8595067649 Simplifying x = 0.8595067649Subproblem 2
x + -0.1388888889 = -0.720617876 Simplifying x + -0.1388888889 = -0.720617876 Reorder the terms: -0.1388888889 + x = -0.720617876 Solving -0.1388888889 + x = -0.720617876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1388888889' to each side of the equation. -0.1388888889 + 0.1388888889 + x = -0.720617876 + 0.1388888889 Combine like terms: -0.1388888889 + 0.1388888889 = 0.0000000000 0.0000000000 + x = -0.720617876 + 0.1388888889 x = -0.720617876 + 0.1388888889 Combine like terms: -0.720617876 + 0.1388888889 = -0.5817289871 x = -0.5817289871 Simplifying x = -0.5817289871Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8595067649, -0.5817289871}Solution
x = {0, 0.8595067649, -0.5817289871}
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