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Simplifying 11x3 + 13x2 + -6x = 0 Reorder the terms: -6x + 13x2 + 11x3 = 0 Solving -6x + 13x2 + 11x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 13x + 11x2) = 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 '(-6 + 13x + 11x2)' equal to zero and attempt to solve: Simplifying -6 + 13x + 11x2 = 0 Solving -6 + 13x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.5454545455 + 1.181818182x + x2 = 0 Move the constant term to the right: Add '0.5454545455' to each side of the equation. -0.5454545455 + 1.181818182x + 0.5454545455 + x2 = 0 + 0.5454545455 Reorder the terms: -0.5454545455 + 0.5454545455 + 1.181818182x + x2 = 0 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + 1.181818182x + x2 = 0 + 0.5454545455 1.181818182x + x2 = 0 + 0.5454545455 Combine like terms: 0 + 0.5454545455 = 0.5454545455 1.181818182x + x2 = 0.5454545455 The x term is 1.181818182x. Take half its coefficient (0.590909091). Square it (0.3491735538) and add it to both sides. Add '0.3491735538' to each side of the equation. 1.181818182x + 0.3491735538 + x2 = 0.5454545455 + 0.3491735538 Reorder the terms: 0.3491735538 + 1.181818182x + x2 = 0.5454545455 + 0.3491735538 Combine like terms: 0.5454545455 + 0.3491735538 = 0.8946280993 0.3491735538 + 1.181818182x + x2 = 0.8946280993 Factor a perfect square on the left side: (x + 0.590909091)(x + 0.590909091) = 0.8946280993 Calculate the square root of the right side: 0.94584782 Break this problem into two subproblems by setting (x + 0.590909091) equal to 0.94584782 and -0.94584782.Subproblem 1
x + 0.590909091 = 0.94584782 Simplifying x + 0.590909091 = 0.94584782 Reorder the terms: 0.590909091 + x = 0.94584782 Solving 0.590909091 + x = 0.94584782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.590909091' to each side of the equation. 0.590909091 + -0.590909091 + x = 0.94584782 + -0.590909091 Combine like terms: 0.590909091 + -0.590909091 = 0.000000000 0.000000000 + x = 0.94584782 + -0.590909091 x = 0.94584782 + -0.590909091 Combine like terms: 0.94584782 + -0.590909091 = 0.354938729 x = 0.354938729 Simplifying x = 0.354938729Subproblem 2
x + 0.590909091 = -0.94584782 Simplifying x + 0.590909091 = -0.94584782 Reorder the terms: 0.590909091 + x = -0.94584782 Solving 0.590909091 + x = -0.94584782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.590909091' to each side of the equation. 0.590909091 + -0.590909091 + x = -0.94584782 + -0.590909091 Combine like terms: 0.590909091 + -0.590909091 = 0.000000000 0.000000000 + x = -0.94584782 + -0.590909091 x = -0.94584782 + -0.590909091 Combine like terms: -0.94584782 + -0.590909091 = -1.536756911 x = -1.536756911 Simplifying x = -1.536756911Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.354938729, -1.536756911}Solution
x = {0, 0.354938729, -1.536756911}
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