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Simplifying 53x3 + -14x2 + -6x = 0 Reorder the terms: -6x + -14x2 + 53x3 = 0 Solving -6x + -14x2 + 53x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + -14x + 53x2) = 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 + -14x + 53x2)' equal to zero and attempt to solve: Simplifying -6 + -14x + 53x2 = 0 Solving -6 + -14x + 53x2 = 0 Begin completing the square. Divide all terms by 53 the coefficient of the squared term: Divide each side by '53'. -0.1132075472 + -0.2641509434x + x2 = 0 Move the constant term to the right: Add '0.1132075472' to each side of the equation. -0.1132075472 + -0.2641509434x + 0.1132075472 + x2 = 0 + 0.1132075472 Reorder the terms: -0.1132075472 + 0.1132075472 + -0.2641509434x + x2 = 0 + 0.1132075472 Combine like terms: -0.1132075472 + 0.1132075472 = 0.0000000000 0.0000000000 + -0.2641509434x + x2 = 0 + 0.1132075472 -0.2641509434x + x2 = 0 + 0.1132075472 Combine like terms: 0 + 0.1132075472 = 0.1132075472 -0.2641509434x + x2 = 0.1132075472 The x term is -0.2641509434x. Take half its coefficient (-0.1320754717). Square it (0.01744393022) and add it to both sides. Add '0.01744393022' to each side of the equation. -0.2641509434x + 0.01744393022 + x2 = 0.1132075472 + 0.01744393022 Reorder the terms: 0.01744393022 + -0.2641509434x + x2 = 0.1132075472 + 0.01744393022 Combine like terms: 0.1132075472 + 0.01744393022 = 0.13065147742 0.01744393022 + -0.2641509434x + x2 = 0.13065147742 Factor a perfect square on the left side: (x + -0.1320754717)(x + -0.1320754717) = 0.13065147742 Calculate the square root of the right side: 0.361457435 Break this problem into two subproblems by setting (x + -0.1320754717) equal to 0.361457435 and -0.361457435.Subproblem 1
x + -0.1320754717 = 0.361457435 Simplifying x + -0.1320754717 = 0.361457435 Reorder the terms: -0.1320754717 + x = 0.361457435 Solving -0.1320754717 + x = 0.361457435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1320754717' to each side of the equation. -0.1320754717 + 0.1320754717 + x = 0.361457435 + 0.1320754717 Combine like terms: -0.1320754717 + 0.1320754717 = 0.0000000000 0.0000000000 + x = 0.361457435 + 0.1320754717 x = 0.361457435 + 0.1320754717 Combine like terms: 0.361457435 + 0.1320754717 = 0.4935329067 x = 0.4935329067 Simplifying x = 0.4935329067Subproblem 2
x + -0.1320754717 = -0.361457435 Simplifying x + -0.1320754717 = -0.361457435 Reorder the terms: -0.1320754717 + x = -0.361457435 Solving -0.1320754717 + x = -0.361457435 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1320754717' to each side of the equation. -0.1320754717 + 0.1320754717 + x = -0.361457435 + 0.1320754717 Combine like terms: -0.1320754717 + 0.1320754717 = 0.0000000000 0.0000000000 + x = -0.361457435 + 0.1320754717 x = -0.361457435 + 0.1320754717 Combine like terms: -0.361457435 + 0.1320754717 = -0.2293819633 x = -0.2293819633 Simplifying x = -0.2293819633Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4935329067, -0.2293819633}Solution
x = {0, 0.4935329067, -0.2293819633}
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