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Simplifying 5619.7x2 + 66595.5x + -46228000 = 0 Reorder the terms: -46228000 + 66595.5x + 5619.7x2 = 0 Solving -46228000 + 66595.5x + 5619.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5619.7 the coefficient of the squared term: Divide each side by '5619.7'. -8226.061889 + 11.85036568x + x2 = 0 Move the constant term to the right: Add '8226.061889' to each side of the equation. -8226.061889 + 11.85036568x + 8226.061889 + x2 = 0 + 8226.061889 Reorder the terms: -8226.061889 + 8226.061889 + 11.85036568x + x2 = 0 + 8226.061889 Combine like terms: -8226.061889 + 8226.061889 = 0.000000 0.000000 + 11.85036568x + x2 = 0 + 8226.061889 11.85036568x + x2 = 0 + 8226.061889 Combine like terms: 0 + 8226.061889 = 8226.061889 11.85036568x + x2 = 8226.061889 The x term is 11.85036568x. Take half its coefficient (5.92518284). Square it (35.10779169) and add it to both sides. Add '35.10779169' to each side of the equation. 11.85036568x + 35.10779169 + x2 = 8226.061889 + 35.10779169 Reorder the terms: 35.10779169 + 11.85036568x + x2 = 8226.061889 + 35.10779169 Combine like terms: 8226.061889 + 35.10779169 = 8261.16968069 35.10779169 + 11.85036568x + x2 = 8261.16968069 Factor a perfect square on the left side: (x + 5.92518284)(x + 5.92518284) = 8261.16968069 Calculate the square root of the right side: 90.890976894 Break this problem into two subproblems by setting (x + 5.92518284) equal to 90.890976894 and -90.890976894.Subproblem 1
x + 5.92518284 = 90.890976894 Simplifying x + 5.92518284 = 90.890976894 Reorder the terms: 5.92518284 + x = 90.890976894 Solving 5.92518284 + x = 90.890976894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.92518284' to each side of the equation. 5.92518284 + -5.92518284 + x = 90.890976894 + -5.92518284 Combine like terms: 5.92518284 + -5.92518284 = 0.00000000 0.00000000 + x = 90.890976894 + -5.92518284 x = 90.890976894 + -5.92518284 Combine like terms: 90.890976894 + -5.92518284 = 84.965794054 x = 84.965794054 Simplifying x = 84.965794054Subproblem 2
x + 5.92518284 = -90.890976894 Simplifying x + 5.92518284 = -90.890976894 Reorder the terms: 5.92518284 + x = -90.890976894 Solving 5.92518284 + x = -90.890976894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.92518284' to each side of the equation. 5.92518284 + -5.92518284 + x = -90.890976894 + -5.92518284 Combine like terms: 5.92518284 + -5.92518284 = 0.00000000 0.00000000 + x = -90.890976894 + -5.92518284 x = -90.890976894 + -5.92518284 Combine like terms: -90.890976894 + -5.92518284 = -96.816159734 x = -96.816159734 Simplifying x = -96.816159734Solution
The solution to the problem is based on the solutions from the subproblems. x = {84.965794054, -96.816159734}
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