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Simplifying 17x2 + 9x + 1 = 0 Reorder the terms: 1 + 9x + 17x2 = 0 Solving 1 + 9x + 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'. 0.05882352941 + 0.5294117647x + x2 = 0 Move the constant term to the right: Add '-0.05882352941' to each side of the equation. 0.05882352941 + 0.5294117647x + -0.05882352941 + x2 = 0 + -0.05882352941 Reorder the terms: 0.05882352941 + -0.05882352941 + 0.5294117647x + x2 = 0 + -0.05882352941 Combine like terms: 0.05882352941 + -0.05882352941 = 0.00000000000 0.00000000000 + 0.5294117647x + x2 = 0 + -0.05882352941 0.5294117647x + x2 = 0 + -0.05882352941 Combine like terms: 0 + -0.05882352941 = -0.05882352941 0.5294117647x + x2 = -0.05882352941 The x term is 0.5294117647x. Take half its coefficient (0.2647058824). Square it (0.07006920418) and add it to both sides. Add '0.07006920418' to each side of the equation. 0.5294117647x + 0.07006920418 + x2 = -0.05882352941 + 0.07006920418 Reorder the terms: 0.07006920418 + 0.5294117647x + x2 = -0.05882352941 + 0.07006920418 Combine like terms: -0.05882352941 + 0.07006920418 = 0.01124567477 0.07006920418 + 0.5294117647x + x2 = 0.01124567477 Factor a perfect square on the left side: (x + 0.2647058824)(x + 0.2647058824) = 0.01124567477 Calculate the square root of the right side: 0.106045626 Break this problem into two subproblems by setting (x + 0.2647058824) equal to 0.106045626 and -0.106045626.Subproblem 1
x + 0.2647058824 = 0.106045626 Simplifying x + 0.2647058824 = 0.106045626 Reorder the terms: 0.2647058824 + x = 0.106045626 Solving 0.2647058824 + x = 0.106045626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2647058824' to each side of the equation. 0.2647058824 + -0.2647058824 + x = 0.106045626 + -0.2647058824 Combine like terms: 0.2647058824 + -0.2647058824 = 0.0000000000 0.0000000000 + x = 0.106045626 + -0.2647058824 x = 0.106045626 + -0.2647058824 Combine like terms: 0.106045626 + -0.2647058824 = -0.1586602564 x = -0.1586602564 Simplifying x = -0.1586602564Subproblem 2
x + 0.2647058824 = -0.106045626 Simplifying x + 0.2647058824 = -0.106045626 Reorder the terms: 0.2647058824 + x = -0.106045626 Solving 0.2647058824 + x = -0.106045626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2647058824' to each side of the equation. 0.2647058824 + -0.2647058824 + x = -0.106045626 + -0.2647058824 Combine like terms: 0.2647058824 + -0.2647058824 = 0.0000000000 0.0000000000 + x = -0.106045626 + -0.2647058824 x = -0.106045626 + -0.2647058824 Combine like terms: -0.106045626 + -0.2647058824 = -0.3707515084 x = -0.3707515084 Simplifying x = -0.3707515084Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1586602564, -0.3707515084}
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