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Simplifying 11x3 + -7x2 + -6x = 0 Reorder the terms: -6x + -7x2 + 11x3 = 0 Solving -6x + -7x2 + 11x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + -7x + 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 + -7x + 11x2)' equal to zero and attempt to solve: Simplifying -6 + -7x + 11x2 = 0 Solving -6 + -7x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.5454545455 + -0.6363636364x + x2 = 0 Move the constant term to the right: Add '0.5454545455' to each side of the equation. -0.5454545455 + -0.6363636364x + 0.5454545455 + x2 = 0 + 0.5454545455 Reorder the terms: -0.5454545455 + 0.5454545455 + -0.6363636364x + x2 = 0 + 0.5454545455 Combine like terms: -0.5454545455 + 0.5454545455 = 0.0000000000 0.0000000000 + -0.6363636364x + x2 = 0 + 0.5454545455 -0.6363636364x + x2 = 0 + 0.5454545455 Combine like terms: 0 + 0.5454545455 = 0.5454545455 -0.6363636364x + x2 = 0.5454545455 The x term is -0.6363636364x. Take half its coefficient (-0.3181818182). Square it (0.1012396694) and add it to both sides. Add '0.1012396694' to each side of the equation. -0.6363636364x + 0.1012396694 + x2 = 0.5454545455 + 0.1012396694 Reorder the terms: 0.1012396694 + -0.6363636364x + x2 = 0.5454545455 + 0.1012396694 Combine like terms: 0.5454545455 + 0.1012396694 = 0.6466942149 0.1012396694 + -0.6363636364x + x2 = 0.6466942149 Factor a perfect square on the left side: (x + -0.3181818182)(x + -0.3181818182) = 0.6466942149 Calculate the square root of the right side: 0.804173001 Break this problem into two subproblems by setting (x + -0.3181818182) equal to 0.804173001 and -0.804173001.Subproblem 1
x + -0.3181818182 = 0.804173001 Simplifying x + -0.3181818182 = 0.804173001 Reorder the terms: -0.3181818182 + x = 0.804173001 Solving -0.3181818182 + x = 0.804173001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + x = 0.804173001 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = 0.804173001 + 0.3181818182 x = 0.804173001 + 0.3181818182 Combine like terms: 0.804173001 + 0.3181818182 = 1.1223548192 x = 1.1223548192 Simplifying x = 1.1223548192Subproblem 2
x + -0.3181818182 = -0.804173001 Simplifying x + -0.3181818182 = -0.804173001 Reorder the terms: -0.3181818182 + x = -0.804173001 Solving -0.3181818182 + x = -0.804173001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + x = -0.804173001 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = -0.804173001 + 0.3181818182 x = -0.804173001 + 0.3181818182 Combine like terms: -0.804173001 + 0.3181818182 = -0.4859911828 x = -0.4859911828 Simplifying x = -0.4859911828Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1223548192, -0.4859911828}Solution
x = {0, 1.1223548192, -0.4859911828}
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