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Simplifying -1600x2 + 4.4145x + 110.3625 = 0 Reorder the terms: 110.3625 + 4.4145x + -1600x2 = 0 Solving 110.3625 + 4.4145x + -1600x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1600 the coefficient of the squared term: Divide each side by '-1600'. -0.0689765625 + -0.0027590625x + x2 = 0 Move the constant term to the right: Add '0.0689765625' to each side of the equation. -0.0689765625 + -0.0027590625x + 0.0689765625 + x2 = 0 + 0.0689765625 Reorder the terms: -0.0689765625 + 0.0689765625 + -0.0027590625x + x2 = 0 + 0.0689765625 Combine like terms: -0.0689765625 + 0.0689765625 = 0.0000000000 0.0000000000 + -0.0027590625x + x2 = 0 + 0.0689765625 -0.0027590625x + x2 = 0 + 0.0689765625 Combine like terms: 0 + 0.0689765625 = 0.0689765625 -0.0027590625x + x2 = 0.0689765625 The x term is -0.0027590625x. Take half its coefficient (-0.00137953125). Square it (0.000001903106470) and add it to both sides. Add '0.000001903106470' to each side of the equation. -0.0027590625x + 0.000001903106470 + x2 = 0.0689765625 + 0.000001903106470 Reorder the terms: 0.000001903106470 + -0.0027590625x + x2 = 0.0689765625 + 0.000001903106470 Combine like terms: 0.0689765625 + 0.000001903106470 = 0.06897846560647 0.000001903106470 + -0.0027590625x + x2 = 0.06897846560647 Factor a perfect square on the left side: (x + -0.00137953125)(x + -0.00137953125) = 0.06897846560647 Calculate the square root of the right side: 0.262637518 Break this problem into two subproblems by setting (x + -0.00137953125) equal to 0.262637518 and -0.262637518.Subproblem 1
x + -0.00137953125 = 0.262637518 Simplifying x + -0.00137953125 = 0.262637518 Reorder the terms: -0.00137953125 + x = 0.262637518 Solving -0.00137953125 + x = 0.262637518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00137953125' to each side of the equation. -0.00137953125 + 0.00137953125 + x = 0.262637518 + 0.00137953125 Combine like terms: -0.00137953125 + 0.00137953125 = 0.00000000000 0.00000000000 + x = 0.262637518 + 0.00137953125 x = 0.262637518 + 0.00137953125 Combine like terms: 0.262637518 + 0.00137953125 = 0.26401704925 x = 0.26401704925 Simplifying x = 0.26401704925Subproblem 2
x + -0.00137953125 = -0.262637518 Simplifying x + -0.00137953125 = -0.262637518 Reorder the terms: -0.00137953125 + x = -0.262637518 Solving -0.00137953125 + x = -0.262637518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00137953125' to each side of the equation. -0.00137953125 + 0.00137953125 + x = -0.262637518 + 0.00137953125 Combine like terms: -0.00137953125 + 0.00137953125 = 0.00000000000 0.00000000000 + x = -0.262637518 + 0.00137953125 x = -0.262637518 + 0.00137953125 Combine like terms: -0.262637518 + 0.00137953125 = -0.26125798675 x = -0.26125798675 Simplifying x = -0.26125798675Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.26401704925, -0.26125798675}
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