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Simplifying 18x3 + 8x2 + 2x = 0 Reorder the terms: 2x + 8x2 + 18x3 = 0 Solving 2x + 8x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(1 + 4x + 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 '(1 + 4x + 9x2)' equal to zero and attempt to solve: Simplifying 1 + 4x + 9x2 = 0 Solving 1 + 4x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + 0.4444444444x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + 0.4444444444x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + 0.4444444444x + x2 = 0 + -0.1111111111 0.4444444444x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 0.4444444444x + x2 = -0.1111111111 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = -0.1111111111 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = -0.1111111111 + 0.04938271604 Combine like terms: -0.1111111111 + 0.04938271604 = -0.06172839506 0.04938271604 + 0.4444444444x + x2 = -0.06172839506 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = -0.06172839506 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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