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Simplifying 54x2 + -10x + -1 = 0 Reorder the terms: -1 + -10x + 54x2 = 0 Solving -1 + -10x + 54x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 54 the coefficient of the squared term: Divide each side by '54'. -0.01851851852 + -0.1851851852x + x2 = 0 Move the constant term to the right: Add '0.01851851852' to each side of the equation. -0.01851851852 + -0.1851851852x + 0.01851851852 + x2 = 0 + 0.01851851852 Reorder the terms: -0.01851851852 + 0.01851851852 + -0.1851851852x + x2 = 0 + 0.01851851852 Combine like terms: -0.01851851852 + 0.01851851852 = 0.00000000000 0.00000000000 + -0.1851851852x + x2 = 0 + 0.01851851852 -0.1851851852x + x2 = 0 + 0.01851851852 Combine like terms: 0 + 0.01851851852 = 0.01851851852 -0.1851851852x + x2 = 0.01851851852 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 = 0.01851851852 + 0.008573388204 Reorder the terms: 0.008573388204 + -0.1851851852x + x2 = 0.01851851852 + 0.008573388204 Combine like terms: 0.01851851852 + 0.008573388204 = 0.027091906724 0.008573388204 + -0.1851851852x + x2 = 0.027091906724 Factor a perfect square on the left side: (x + -0.0925925926)(x + -0.0925925926) = 0.027091906724 Calculate the square root of the right side: 0.164596193 Break this problem into two subproblems by setting (x + -0.0925925926) equal to 0.164596193 and -0.164596193.Subproblem 1
x + -0.0925925926 = 0.164596193 Simplifying x + -0.0925925926 = 0.164596193 Reorder the terms: -0.0925925926 + x = 0.164596193 Solving -0.0925925926 + x = 0.164596193 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 = 0.164596193 + 0.0925925926 Combine like terms: -0.0925925926 + 0.0925925926 = 0.0000000000 0.0000000000 + x = 0.164596193 + 0.0925925926 x = 0.164596193 + 0.0925925926 Combine like terms: 0.164596193 + 0.0925925926 = 0.2571887856 x = 0.2571887856 Simplifying x = 0.2571887856Subproblem 2
x + -0.0925925926 = -0.164596193 Simplifying x + -0.0925925926 = -0.164596193 Reorder the terms: -0.0925925926 + x = -0.164596193 Solving -0.0925925926 + x = -0.164596193 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 = -0.164596193 + 0.0925925926 Combine like terms: -0.0925925926 + 0.0925925926 = 0.0000000000 0.0000000000 + x = -0.164596193 + 0.0925925926 x = -0.164596193 + 0.0925925926 Combine like terms: -0.164596193 + 0.0925925926 = -0.0720036004 x = -0.0720036004 Simplifying x = -0.0720036004Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2571887856, -0.0720036004}
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