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Simplifying 11x3 + -9x2 + -10x = 0 Reorder the terms: -10x + -9x2 + 11x3 = 0 Solving -10x + -9x2 + 11x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-10 + -9x + 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 '(-10 + -9x + 11x2)' equal to zero and attempt to solve: Simplifying -10 + -9x + 11x2 = 0 Solving -10 + -9x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.9090909091 + -0.8181818182x + x2 = 0 Move the constant term to the right: Add '0.9090909091' to each side of the equation. -0.9090909091 + -0.8181818182x + 0.9090909091 + x2 = 0 + 0.9090909091 Reorder the terms: -0.9090909091 + 0.9090909091 + -0.8181818182x + x2 = 0 + 0.9090909091 Combine like terms: -0.9090909091 + 0.9090909091 = 0.0000000000 0.0000000000 + -0.8181818182x + x2 = 0 + 0.9090909091 -0.8181818182x + x2 = 0 + 0.9090909091 Combine like terms: 0 + 0.9090909091 = 0.9090909091 -0.8181818182x + x2 = 0.9090909091 The x term is -0.8181818182x. Take half its coefficient (-0.4090909091). Square it (0.1673553719) and add it to both sides. Add '0.1673553719' to each side of the equation. -0.8181818182x + 0.1673553719 + x2 = 0.9090909091 + 0.1673553719 Reorder the terms: 0.1673553719 + -0.8181818182x + x2 = 0.9090909091 + 0.1673553719 Combine like terms: 0.9090909091 + 0.1673553719 = 1.076446281 0.1673553719 + -0.8181818182x + x2 = 1.076446281 Factor a perfect square on the left side: (x + -0.4090909091)(x + -0.4090909091) = 1.076446281 Calculate the square root of the right side: 1.037519292 Break this problem into two subproblems by setting (x + -0.4090909091) equal to 1.037519292 and -1.037519292.Subproblem 1
x + -0.4090909091 = 1.037519292 Simplifying x + -0.4090909091 = 1.037519292 Reorder the terms: -0.4090909091 + x = 1.037519292 Solving -0.4090909091 + x = 1.037519292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4090909091' to each side of the equation. -0.4090909091 + 0.4090909091 + x = 1.037519292 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + x = 1.037519292 + 0.4090909091 x = 1.037519292 + 0.4090909091 Combine like terms: 1.037519292 + 0.4090909091 = 1.4466102011 x = 1.4466102011 Simplifying x = 1.4466102011Subproblem 2
x + -0.4090909091 = -1.037519292 Simplifying x + -0.4090909091 = -1.037519292 Reorder the terms: -0.4090909091 + x = -1.037519292 Solving -0.4090909091 + x = -1.037519292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4090909091' to each side of the equation. -0.4090909091 + 0.4090909091 + x = -1.037519292 + 0.4090909091 Combine like terms: -0.4090909091 + 0.4090909091 = 0.0000000000 0.0000000000 + x = -1.037519292 + 0.4090909091 x = -1.037519292 + 0.4090909091 Combine like terms: -1.037519292 + 0.4090909091 = -0.6284283829 x = -0.6284283829 Simplifying x = -0.6284283829Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4466102011, -0.6284283829}Solution
x = {0, 1.4466102011, -0.6284283829}
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