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Simplifying 16x2 + -9x + 1 = 0 Reorder the terms: 1 + -9x + 16x2 = 0 Solving 1 + -9x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.0625 + -0.5625x + x2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + -0.5625x + -0.0625 + x2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + -0.5625x + x2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + -0.5625x + x2 = 0 + -0.0625 -0.5625x + x2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 -0.5625x + x2 = -0.0625 The x term is -0.5625x. Take half its coefficient (-0.28125). Square it (0.0791015625) and add it to both sides. Add '0.0791015625' to each side of the equation. -0.5625x + 0.0791015625 + x2 = -0.0625 + 0.0791015625 Reorder the terms: 0.0791015625 + -0.5625x + x2 = -0.0625 + 0.0791015625 Combine like terms: -0.0625 + 0.0791015625 = 0.0166015625 0.0791015625 + -0.5625x + x2 = 0.0166015625 Factor a perfect square on the left side: (x + -0.28125)(x + -0.28125) = 0.0166015625 Calculate the square root of the right side: 0.128847051 Break this problem into two subproblems by setting (x + -0.28125) equal to 0.128847051 and -0.128847051.Subproblem 1
x + -0.28125 = 0.128847051 Simplifying x + -0.28125 = 0.128847051 Reorder the terms: -0.28125 + x = 0.128847051 Solving -0.28125 + x = 0.128847051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = 0.128847051 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = 0.128847051 + 0.28125 x = 0.128847051 + 0.28125 Combine like terms: 0.128847051 + 0.28125 = 0.410097051 x = 0.410097051 Simplifying x = 0.410097051Subproblem 2
x + -0.28125 = -0.128847051 Simplifying x + -0.28125 = -0.128847051 Reorder the terms: -0.28125 + x = -0.128847051 Solving -0.28125 + x = -0.128847051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28125' to each side of the equation. -0.28125 + 0.28125 + x = -0.128847051 + 0.28125 Combine like terms: -0.28125 + 0.28125 = 0.00000 0.00000 + x = -0.128847051 + 0.28125 x = -0.128847051 + 0.28125 Combine like terms: -0.128847051 + 0.28125 = 0.152402949 x = 0.152402949 Simplifying x = 0.152402949Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.410097051, 0.152402949}
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