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Simplifying 17x2 + 39x + 17 = 0 Reorder the terms: 17 + 39x + 17x2 = 0 Solving 17 + 39x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. 1 + 2.294117647x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 2.294117647x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 2.294117647x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2.294117647x + x2 = 0 + -1 2.294117647x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 2.294117647x + x2 = -1 The x term is 2.294117647x. Take half its coefficient (1.147058824). Square it (1.315743946) and add it to both sides. Add '1.315743946' to each side of the equation. 2.294117647x + 1.315743946 + x2 = -1 + 1.315743946 Reorder the terms: 1.315743946 + 2.294117647x + x2 = -1 + 1.315743946 Combine like terms: -1 + 1.315743946 = 0.315743946 1.315743946 + 2.294117647x + x2 = 0.315743946 Factor a perfect square on the left side: (x + 1.147058824)(x + 1.147058824) = 0.315743946 Calculate the square root of the right side: 0.561910977 Break this problem into two subproblems by setting (x + 1.147058824) equal to 0.561910977 and -0.561910977.Subproblem 1
x + 1.147058824 = 0.561910977 Simplifying x + 1.147058824 = 0.561910977 Reorder the terms: 1.147058824 + x = 0.561910977 Solving 1.147058824 + x = 0.561910977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.147058824' to each side of the equation. 1.147058824 + -1.147058824 + x = 0.561910977 + -1.147058824 Combine like terms: 1.147058824 + -1.147058824 = 0.000000000 0.000000000 + x = 0.561910977 + -1.147058824 x = 0.561910977 + -1.147058824 Combine like terms: 0.561910977 + -1.147058824 = -0.585147847 x = -0.585147847 Simplifying x = -0.585147847Subproblem 2
x + 1.147058824 = -0.561910977 Simplifying x + 1.147058824 = -0.561910977 Reorder the terms: 1.147058824 + x = -0.561910977 Solving 1.147058824 + x = -0.561910977 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.147058824' to each side of the equation. 1.147058824 + -1.147058824 + x = -0.561910977 + -1.147058824 Combine like terms: 1.147058824 + -1.147058824 = 0.000000000 0.000000000 + x = -0.561910977 + -1.147058824 x = -0.561910977 + -1.147058824 Combine like terms: -0.561910977 + -1.147058824 = -1.708969801 x = -1.708969801 Simplifying x = -1.708969801Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.585147847, -1.708969801}
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