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Simplifying 10x(11x2 + 5x + 4) = 0 Reorder the terms: 10x(4 + 5x + 11x2) = 0 (4 * 10x + 5x * 10x + 11x2 * 10x) = 0 (40x + 50x2 + 110x3) = 0 Solving 40x + 50x2 + 110x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10x'. 10x(4 + 5x + 11x2) = 0 Ignore the factor 10.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 '(4 + 5x + 11x2)' equal to zero and attempt to solve: Simplifying 4 + 5x + 11x2 = 0 Solving 4 + 5x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.3636363636 + 0.4545454545x + x2 = 0 Move the constant term to the right: Add '-0.3636363636' to each side of the equation. 0.3636363636 + 0.4545454545x + -0.3636363636 + x2 = 0 + -0.3636363636 Reorder the terms: 0.3636363636 + -0.3636363636 + 0.4545454545x + x2 = 0 + -0.3636363636 Combine like terms: 0.3636363636 + -0.3636363636 = 0.0000000000 0.0000000000 + 0.4545454545x + x2 = 0 + -0.3636363636 0.4545454545x + x2 = 0 + -0.3636363636 Combine like terms: 0 + -0.3636363636 = -0.3636363636 0.4545454545x + x2 = -0.3636363636 The x term is 0.4545454545x. Take half its coefficient (0.2272727273). Square it (0.05165289257) and add it to both sides. Add '0.05165289257' to each side of the equation. 0.4545454545x + 0.05165289257 + x2 = -0.3636363636 + 0.05165289257 Reorder the terms: 0.05165289257 + 0.4545454545x + x2 = -0.3636363636 + 0.05165289257 Combine like terms: -0.3636363636 + 0.05165289257 = -0.31198347103 0.05165289257 + 0.4545454545x + x2 = -0.31198347103 Factor a perfect square on the left side: (x + 0.2272727273)(x + 0.2272727273) = -0.31198347103 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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