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Simplifying (11x2 + 7x + -14)(x) = 0 Reorder the terms: (-14 + 7x + 11x2)(x) = 0 Reorder the terms for easier multiplication: x(-14 + 7x + 11x2) = 0 (-14 * x + 7x * x + 11x2 * x) = 0 (-14x + 7x2 + 11x3) = 0 Solving -14x + 7x2 + 11x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-14 + 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 '(-14 + 7x + 11x2)' equal to zero and attempt to solve: Simplifying -14 + 7x + 11x2 = 0 Solving -14 + 7x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.272727273 + 0.6363636364x + x2 = 0 Move the constant term to the right: Add '1.272727273' to each side of the equation. -1.272727273 + 0.6363636364x + 1.272727273 + x2 = 0 + 1.272727273 Reorder the terms: -1.272727273 + 1.272727273 + 0.6363636364x + x2 = 0 + 1.272727273 Combine like terms: -1.272727273 + 1.272727273 = 0.000000000 0.000000000 + 0.6363636364x + x2 = 0 + 1.272727273 0.6363636364x + x2 = 0 + 1.272727273 Combine like terms: 0 + 1.272727273 = 1.272727273 0.6363636364x + x2 = 1.272727273 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 = 1.272727273 + 0.1012396694 Reorder the terms: 0.1012396694 + 0.6363636364x + x2 = 1.272727273 + 0.1012396694 Combine like terms: 1.272727273 + 0.1012396694 = 1.3739669424 0.1012396694 + 0.6363636364x + x2 = 1.3739669424 Factor a perfect square on the left side: (x + 0.3181818182)(x + 0.3181818182) = 1.3739669424 Calculate the square root of the right side: 1.17216336 Break this problem into two subproblems by setting (x + 0.3181818182) equal to 1.17216336 and -1.17216336.Subproblem 1
x + 0.3181818182 = 1.17216336 Simplifying x + 0.3181818182 = 1.17216336 Reorder the terms: 0.3181818182 + x = 1.17216336 Solving 0.3181818182 + x = 1.17216336 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 = 1.17216336 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + x = 1.17216336 + -0.3181818182 x = 1.17216336 + -0.3181818182 Combine like terms: 1.17216336 + -0.3181818182 = 0.8539815418 x = 0.8539815418 Simplifying x = 0.8539815418Subproblem 2
x + 0.3181818182 = -1.17216336 Simplifying x + 0.3181818182 = -1.17216336 Reorder the terms: 0.3181818182 + x = -1.17216336 Solving 0.3181818182 + x = -1.17216336 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 = -1.17216336 + -0.3181818182 Combine like terms: 0.3181818182 + -0.3181818182 = 0.0000000000 0.0000000000 + x = -1.17216336 + -0.3181818182 x = -1.17216336 + -0.3181818182 Combine like terms: -1.17216336 + -0.3181818182 = -1.4903451782 x = -1.4903451782 Simplifying x = -1.4903451782Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8539815418, -1.4903451782}Solution
x = {0, 0.8539815418, -1.4903451782}
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