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Simplifying 16x2 + 1090x + -3.4 = 0 Reorder the terms: -3.4 + 1090x + 16x2 = 0 Solving -3.4 + 1090x + 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'. -0.2125 + 68.125x + x2 = 0 Move the constant term to the right: Add '0.2125' to each side of the equation. -0.2125 + 68.125x + 0.2125 + x2 = 0 + 0.2125 Reorder the terms: -0.2125 + 0.2125 + 68.125x + x2 = 0 + 0.2125 Combine like terms: -0.2125 + 0.2125 = 0.0000 0.0000 + 68.125x + x2 = 0 + 0.2125 68.125x + x2 = 0 + 0.2125 Combine like terms: 0 + 0.2125 = 0.2125 68.125x + x2 = 0.2125 The x term is 68.125x. Take half its coefficient (34.0625). Square it (1160.253906) and add it to both sides. Add '1160.253906' to each side of the equation. 68.125x + 1160.253906 + x2 = 0.2125 + 1160.253906 Reorder the terms: 1160.253906 + 68.125x + x2 = 0.2125 + 1160.253906 Combine like terms: 0.2125 + 1160.253906 = 1160.466406 1160.253906 + 68.125x + x2 = 1160.466406 Factor a perfect square on the left side: (x + 34.0625)(x + 34.0625) = 1160.466406 Calculate the square root of the right side: 34.06561912 Break this problem into two subproblems by setting (x + 34.0625) equal to 34.06561912 and -34.06561912.Subproblem 1
x + 34.0625 = 34.06561912 Simplifying x + 34.0625 = 34.06561912 Reorder the terms: 34.0625 + x = 34.06561912 Solving 34.0625 + x = 34.06561912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.0625' to each side of the equation. 34.0625 + -34.0625 + x = 34.06561912 + -34.0625 Combine like terms: 34.0625 + -34.0625 = 0.0000 0.0000 + x = 34.06561912 + -34.0625 x = 34.06561912 + -34.0625 Combine like terms: 34.06561912 + -34.0625 = 0.00311912 x = 0.00311912 Simplifying x = 0.00311912Subproblem 2
x + 34.0625 = -34.06561912 Simplifying x + 34.0625 = -34.06561912 Reorder the terms: 34.0625 + x = -34.06561912 Solving 34.0625 + x = -34.06561912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.0625' to each side of the equation. 34.0625 + -34.0625 + x = -34.06561912 + -34.0625 Combine like terms: 34.0625 + -34.0625 = 0.0000 0.0000 + x = -34.06561912 + -34.0625 x = -34.06561912 + -34.0625 Combine like terms: -34.06561912 + -34.0625 = -68.12811912 x = -68.12811912 Simplifying x = -68.12811912Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00311912, -68.12811912}
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