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Simplifying x(7x + 18x2 + 1) = 0 Reorder the terms: x(1 + 7x + 18x2) = 0 (1 * x + 7x * x + 18x2 * x) = 0 (1x + 7x2 + 18x3) = 0 Solving 1x + 7x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 7x + 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 '(1 + 7x + 18x2)' equal to zero and attempt to solve: Simplifying 1 + 7x + 18x2 = 0 Solving 1 + 7x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.05555555556 + 0.3888888889x + x2 = 0 Move the constant term to the right: Add '-0.05555555556' to each side of the equation. 0.05555555556 + 0.3888888889x + -0.05555555556 + x2 = 0 + -0.05555555556 Reorder the terms: 0.05555555556 + -0.05555555556 + 0.3888888889x + x2 = 0 + -0.05555555556 Combine like terms: 0.05555555556 + -0.05555555556 = 0.00000000000 0.00000000000 + 0.3888888889x + x2 = 0 + -0.05555555556 0.3888888889x + x2 = 0 + -0.05555555556 Combine like terms: 0 + -0.05555555556 = -0.05555555556 0.3888888889x + x2 = -0.05555555556 The x term is 0.3888888889x. Take half its coefficient (0.1944444445). Square it (0.03780864200) and add it to both sides. Add '0.03780864200' to each side of the equation. 0.3888888889x + 0.03780864200 + x2 = -0.05555555556 + 0.03780864200 Reorder the terms: 0.03780864200 + 0.3888888889x + x2 = -0.05555555556 + 0.03780864200 Combine like terms: -0.05555555556 + 0.03780864200 = -0.01774691356 0.03780864200 + 0.3888888889x + x2 = -0.01774691356 Factor a perfect square on the left side: (x + 0.1944444445)(x + 0.1944444445) = -0.01774691356 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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