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Simplifying 54x3 + -10x2 + -8x = 0 Reorder the terms: -8x + -10x2 + 54x3 = 0 Solving -8x + -10x2 + 54x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-4 + -5x + 27x2) = 0 Ignore the factor 2.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 + 27x2)' equal to zero and attempt to solve: Simplifying -4 + -5x + 27x2 = 0 Solving -4 + -5x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.1481481481 + -0.1851851852x + x2 = 0 Move the constant term to the right: Add '0.1481481481' to each side of the equation. -0.1481481481 + -0.1851851852x + 0.1481481481 + x2 = 0 + 0.1481481481 Reorder the terms: -0.1481481481 + 0.1481481481 + -0.1851851852x + x2 = 0 + 0.1481481481 Combine like terms: -0.1481481481 + 0.1481481481 = 0.0000000000 0.0000000000 + -0.1851851852x + x2 = 0 + 0.1481481481 -0.1851851852x + x2 = 0 + 0.1481481481 Combine like terms: 0 + 0.1481481481 = 0.1481481481 -0.1851851852x + x2 = 0.1481481481 The x term is -0.1851851852x. Take half its coefficient (-0.0925925926). Square it (0.008573388204) and add it to both sides. Add '0.008573388204' to each side of the equation. -0.1851851852x + 0.008573388204 + x2 = 0.1481481481 + 0.008573388204 Reorder the terms: 0.008573388204 + -0.1851851852x + x2 = 0.1481481481 + 0.008573388204 Combine like terms: 0.1481481481 + 0.008573388204 = 0.156721536304 0.008573388204 + -0.1851851852x + x2 = 0.156721536304 Factor a perfect square on the left side: (x + -0.0925925926)(x + -0.0925925926) = 0.156721536304 Calculate the square root of the right side: 0.39588071 Break this problem into two subproblems by setting (x + -0.0925925926) equal to 0.39588071 and -0.39588071.Subproblem 1
x + -0.0925925926 = 0.39588071 Simplifying x + -0.0925925926 = 0.39588071 Reorder the terms: -0.0925925926 + x = 0.39588071 Solving -0.0925925926 + x = 0.39588071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0925925926' to each side of the equation. -0.0925925926 + 0.0925925926 + x = 0.39588071 + 0.0925925926 Combine like terms: -0.0925925926 + 0.0925925926 = 0.0000000000 0.0000000000 + x = 0.39588071 + 0.0925925926 x = 0.39588071 + 0.0925925926 Combine like terms: 0.39588071 + 0.0925925926 = 0.4884733026 x = 0.4884733026 Simplifying x = 0.4884733026Subproblem 2
x + -0.0925925926 = -0.39588071 Simplifying x + -0.0925925926 = -0.39588071 Reorder the terms: -0.0925925926 + x = -0.39588071 Solving -0.0925925926 + x = -0.39588071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0925925926' to each side of the equation. -0.0925925926 + 0.0925925926 + x = -0.39588071 + 0.0925925926 Combine like terms: -0.0925925926 + 0.0925925926 = 0.0000000000 0.0000000000 + x = -0.39588071 + 0.0925925926 x = -0.39588071 + 0.0925925926 Combine like terms: -0.39588071 + 0.0925925926 = -0.3032881174 x = -0.3032881174 Simplifying x = -0.3032881174Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4884733026, -0.3032881174}Solution
x = {0, 0.4884733026, -0.3032881174}
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