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Simplifying 54x * x + -1x + -29 = 0 Multiply x * x 54x2 + -1x + -29 = 0 Reorder the terms: -29 + -1x + 54x2 = 0 Solving -29 + -1x + 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'. -0.537037037 + -0.01851851852x + x2 = 0 Move the constant term to the right: Add '0.537037037' to each side of the equation. -0.537037037 + -0.01851851852x + 0.537037037 + x2 = 0 + 0.537037037 Reorder the terms: -0.537037037 + 0.537037037 + -0.01851851852x + x2 = 0 + 0.537037037 Combine like terms: -0.537037037 + 0.537037037 = 0.000000000 0.000000000 + -0.01851851852x + x2 = 0 + 0.537037037 -0.01851851852x + x2 = 0 + 0.537037037 Combine like terms: 0 + 0.537037037 = 0.537037037 -0.01851851852x + x2 = 0.537037037 The x term is -0.01851851852x. Take half its coefficient (-0.00925925926). Square it (0.00008573388204) and add it to both sides. Add '0.00008573388204' to each side of the equation. -0.01851851852x + 0.00008573388204 + x2 = 0.537037037 + 0.00008573388204 Reorder the terms: 0.00008573388204 + -0.01851851852x + x2 = 0.537037037 + 0.00008573388204 Combine like terms: 0.537037037 + 0.00008573388204 = 0.53712277088204 0.00008573388204 + -0.01851851852x + x2 = 0.53712277088204 Factor a perfect square on the left side: (x + -0.00925925926)(x + -0.00925925926) = 0.53712277088204 Calculate the square root of the right side: 0.732886602 Break this problem into two subproblems by setting (x + -0.00925925926) equal to 0.732886602 and -0.732886602.Subproblem 1
x + -0.00925925926 = 0.732886602 Simplifying x + -0.00925925926 = 0.732886602 Reorder the terms: -0.00925925926 + x = 0.732886602 Solving -0.00925925926 + x = 0.732886602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00925925926' to each side of the equation. -0.00925925926 + 0.00925925926 + x = 0.732886602 + 0.00925925926 Combine like terms: -0.00925925926 + 0.00925925926 = 0.00000000000 0.00000000000 + x = 0.732886602 + 0.00925925926 x = 0.732886602 + 0.00925925926 Combine like terms: 0.732886602 + 0.00925925926 = 0.74214586126 x = 0.74214586126 Simplifying x = 0.74214586126Subproblem 2
x + -0.00925925926 = -0.732886602 Simplifying x + -0.00925925926 = -0.732886602 Reorder the terms: -0.00925925926 + x = -0.732886602 Solving -0.00925925926 + x = -0.732886602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00925925926' to each side of the equation. -0.00925925926 + 0.00925925926 + x = -0.732886602 + 0.00925925926 Combine like terms: -0.00925925926 + 0.00925925926 = 0.00000000000 0.00000000000 + x = -0.732886602 + 0.00925925926 x = -0.732886602 + 0.00925925926 Combine like terms: -0.732886602 + 0.00925925926 = -0.72362734274 x = -0.72362734274 Simplifying x = -0.72362734274Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.74214586126, -0.72362734274}
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