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Simplifying 18x3 + 18x2 + x = 0 Reorder the terms: x + 18x2 + 18x3 = 0 Solving x + 18x2 + 18x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(1 + 18x + 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 + 18x + 18x2)' equal to zero and attempt to solve: Simplifying 1 + 18x + 18x2 = 0 Solving 1 + 18x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.05555555556 + x + x2 = 0 Move the constant term to the right: Add '-0.05555555556' to each side of the equation. 0.05555555556 + x + -0.05555555556 + x2 = 0 + -0.05555555556 Reorder the terms: 0.05555555556 + -0.05555555556 + x + x2 = 0 + -0.05555555556 Combine like terms: 0.05555555556 + -0.05555555556 = 0.00000000000 0.00000000000 + x + x2 = 0 + -0.05555555556 x + x2 = 0 + -0.05555555556 Combine like terms: 0 + -0.05555555556 = -0.05555555556 x + x2 = -0.05555555556 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -0.05555555556 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.05555555556 + 0.25 Combine like terms: -0.05555555556 + 0.25 = 0.19444444444 1.25 + x2 = 0.19444444444 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.19444444444 Calculate the square root of the right side: 0.440958552 Break this problem into two subproblems by setting (x + 0.5) equal to 0.440958552 and -0.440958552.Subproblem 1
x + 0.5 = 0.440958552 Simplifying x + 0.5 = 0.440958552 Reorder the terms: 0.5 + x = 0.440958552 Solving 0.5 + x = 0.440958552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.440958552 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.440958552 + -0.5 x = 0.440958552 + -0.5 Combine like terms: 0.440958552 + -0.5 = -0.059041448 x = -0.059041448 Simplifying x = -0.059041448Subproblem 2
x + 0.5 = -0.440958552 Simplifying x + 0.5 = -0.440958552 Reorder the terms: 0.5 + x = -0.440958552 Solving 0.5 + x = -0.440958552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.440958552 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.440958552 + -0.5 x = -0.440958552 + -0.5 Combine like terms: -0.440958552 + -0.5 = -0.940958552 x = -0.940958552 Simplifying x = -0.940958552Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.059041448, -0.940958552}Solution
x = {0, -0.059041448, -0.940958552}
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