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Simplifying -396x3 + -108x2 + 108x = 0 Reorder the terms: 108x + -108x2 + -396x3 = 0 Solving 108x + -108x2 + -396x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '36x'. 36x(3 + -3x + -11x2) = 0 Ignore the factor 36.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 '(3 + -3x + -11x2)' equal to zero and attempt to solve: Simplifying 3 + -3x + -11x2 = 0 Solving 3 + -3x + -11x2 = 0 Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -0.2727272727 + 0.2727272727x + x2 = 0 Move the constant term to the right: Add '0.2727272727' to each side of the equation. -0.2727272727 + 0.2727272727x + 0.2727272727 + x2 = 0 + 0.2727272727 Reorder the terms: -0.2727272727 + 0.2727272727 + 0.2727272727x + x2 = 0 + 0.2727272727 Combine like terms: -0.2727272727 + 0.2727272727 = 0.0000000000 0.0000000000 + 0.2727272727x + x2 = 0 + 0.2727272727 0.2727272727x + x2 = 0 + 0.2727272727 Combine like terms: 0 + 0.2727272727 = 0.2727272727 0.2727272727x + x2 = 0.2727272727 The x term is 0.2727272727x. Take half its coefficient (0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. 0.2727272727x + 0.01859504133 + x2 = 0.2727272727 + 0.01859504133 Reorder the terms: 0.01859504133 + 0.2727272727x + x2 = 0.2727272727 + 0.01859504133 Combine like terms: 0.2727272727 + 0.01859504133 = 0.29132231403 0.01859504133 + 0.2727272727x + x2 = 0.29132231403 Factor a perfect square on the left side: (x + 0.1363636364)(x + 0.1363636364) = 0.29132231403 Calculate the square root of the right side: 0.539742822 Break this problem into two subproblems by setting (x + 0.1363636364) equal to 0.539742822 and -0.539742822.Subproblem 1
x + 0.1363636364 = 0.539742822 Simplifying x + 0.1363636364 = 0.539742822 Reorder the terms: 0.1363636364 + x = 0.539742822 Solving 0.1363636364 + x = 0.539742822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + x = 0.539742822 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = 0.539742822 + -0.1363636364 x = 0.539742822 + -0.1363636364 Combine like terms: 0.539742822 + -0.1363636364 = 0.4033791856 x = 0.4033791856 Simplifying x = 0.4033791856Subproblem 2
x + 0.1363636364 = -0.539742822 Simplifying x + 0.1363636364 = -0.539742822 Reorder the terms: 0.1363636364 + x = -0.539742822 Solving 0.1363636364 + x = -0.539742822 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1363636364' to each side of the equation. 0.1363636364 + -0.1363636364 + x = -0.539742822 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + x = -0.539742822 + -0.1363636364 x = -0.539742822 + -0.1363636364 Combine like terms: -0.539742822 + -0.1363636364 = -0.6761064584 x = -0.6761064584 Simplifying x = -0.6761064584Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4033791856, -0.6761064584}Solution
x = {0, 0.4033791856, -0.6761064584}
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