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Simplifying 8x2 + -29x + 1 = 0 Reorder the terms: 1 + -29x + 8x2 = 0 Solving 1 + -29x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.125 + -3.625x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -3.625x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -3.625x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -3.625x + x2 = 0 + -0.125 -3.625x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -3.625x + x2 = -0.125 The x term is -3.625x. Take half its coefficient (-1.8125). Square it (3.28515625) and add it to both sides. Add '3.28515625' to each side of the equation. -3.625x + 3.28515625 + x2 = -0.125 + 3.28515625 Reorder the terms: 3.28515625 + -3.625x + x2 = -0.125 + 3.28515625 Combine like terms: -0.125 + 3.28515625 = 3.16015625 3.28515625 + -3.625x + x2 = 3.16015625 Factor a perfect square on the left side: (x + -1.8125)(x + -1.8125) = 3.16015625 Calculate the square root of the right side: 1.777682832 Break this problem into two subproblems by setting (x + -1.8125) equal to 1.777682832 and -1.777682832.Subproblem 1
x + -1.8125 = 1.777682832 Simplifying x + -1.8125 = 1.777682832 Reorder the terms: -1.8125 + x = 1.777682832 Solving -1.8125 + x = 1.777682832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + x = 1.777682832 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + x = 1.777682832 + 1.8125 x = 1.777682832 + 1.8125 Combine like terms: 1.777682832 + 1.8125 = 3.590182832 x = 3.590182832 Simplifying x = 3.590182832Subproblem 2
x + -1.8125 = -1.777682832 Simplifying x + -1.8125 = -1.777682832 Reorder the terms: -1.8125 + x = -1.777682832 Solving -1.8125 + x = -1.777682832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8125' to each side of the equation. -1.8125 + 1.8125 + x = -1.777682832 + 1.8125 Combine like terms: -1.8125 + 1.8125 = 0.0000 0.0000 + x = -1.777682832 + 1.8125 x = -1.777682832 + 1.8125 Combine like terms: -1.777682832 + 1.8125 = 0.034817168 x = 0.034817168 Simplifying x = 0.034817168Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.590182832, 0.034817168}
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