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Simplifying x(9x2 + 4x + 3) = 0 Reorder the terms: x(3 + 4x + 9x2) = 0 (3 * x + 4x * x + 9x2 * x) = 0 (3x + 4x2 + 9x3) = 0 Solving 3x + 4x2 + 9x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(3 + 4x + 9x2) = 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 '(3 + 4x + 9x2)' equal to zero and attempt to solve: Simplifying 3 + 4x + 9x2 = 0 Solving 3 + 4x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.3333333333 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + 0.4444444444x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + 0.4444444444x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + 0.4444444444x + x2 = 0 + -0.3333333333 0.4444444444x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 0.4444444444x + x2 = -0.3333333333 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 = -0.3333333333 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = -0.3333333333 + 0.04938271604 Combine like terms: -0.3333333333 + 0.04938271604 = -0.28395061726 0.04938271604 + 0.4444444444x + x2 = -0.28395061726 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = -0.28395061726 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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