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Simplifying 128x2 + 7x + -1 = 0 Reorder the terms: -1 + 7x + 128x2 = 0 Solving -1 + 7x + 128x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 128 the coefficient of the squared term: Divide each side by '128'. -0.0078125 + 0.0546875x + x2 = 0 Move the constant term to the right: Add '0.0078125' to each side of the equation. -0.0078125 + 0.0546875x + 0.0078125 + x2 = 0 + 0.0078125 Reorder the terms: -0.0078125 + 0.0078125 + 0.0546875x + x2 = 0 + 0.0078125 Combine like terms: -0.0078125 + 0.0078125 = 0.0000000 0.0000000 + 0.0546875x + x2 = 0 + 0.0078125 0.0546875x + x2 = 0 + 0.0078125 Combine like terms: 0 + 0.0078125 = 0.0078125 0.0546875x + x2 = 0.0078125 The x term is 0.0546875x. Take half its coefficient (0.02734375). Square it (0.0007476806641) and add it to both sides. Add '0.0007476806641' to each side of the equation. 0.0546875x + 0.0007476806641 + x2 = 0.0078125 + 0.0007476806641 Reorder the terms: 0.0007476806641 + 0.0546875x + x2 = 0.0078125 + 0.0007476806641 Combine like terms: 0.0078125 + 0.0007476806641 = 0.0085601806641 0.0007476806641 + 0.0546875x + x2 = 0.0085601806641 Factor a perfect square on the left side: (x + 0.02734375)(x + 0.02734375) = 0.0085601806641 Calculate the square root of the right side: 0.092521244 Break this problem into two subproblems by setting (x + 0.02734375) equal to 0.092521244 and -0.092521244.Subproblem 1
x + 0.02734375 = 0.092521244 Simplifying x + 0.02734375 = 0.092521244 Reorder the terms: 0.02734375 + x = 0.092521244 Solving 0.02734375 + x = 0.092521244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02734375' to each side of the equation. 0.02734375 + -0.02734375 + x = 0.092521244 + -0.02734375 Combine like terms: 0.02734375 + -0.02734375 = 0.00000000 0.00000000 + x = 0.092521244 + -0.02734375 x = 0.092521244 + -0.02734375 Combine like terms: 0.092521244 + -0.02734375 = 0.065177494 x = 0.065177494 Simplifying x = 0.065177494Subproblem 2
x + 0.02734375 = -0.092521244 Simplifying x + 0.02734375 = -0.092521244 Reorder the terms: 0.02734375 + x = -0.092521244 Solving 0.02734375 + x = -0.092521244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02734375' to each side of the equation. 0.02734375 + -0.02734375 + x = -0.092521244 + -0.02734375 Combine like terms: 0.02734375 + -0.02734375 = 0.00000000 0.00000000 + x = -0.092521244 + -0.02734375 x = -0.092521244 + -0.02734375 Combine like terms: -0.092521244 + -0.02734375 = -0.119864994 x = -0.119864994 Simplifying x = -0.119864994Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.065177494, -0.119864994}
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