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Simplifying 36x2 + -476x + -2461 = 0 Reorder the terms: -2461 + -476x + 36x2 = 0 Solving -2461 + -476x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -68.36111111 + -13.22222222x + x2 = 0 Move the constant term to the right: Add '68.36111111' to each side of the equation. -68.36111111 + -13.22222222x + 68.36111111 + x2 = 0 + 68.36111111 Reorder the terms: -68.36111111 + 68.36111111 + -13.22222222x + x2 = 0 + 68.36111111 Combine like terms: -68.36111111 + 68.36111111 = 0.00000000 0.00000000 + -13.22222222x + x2 = 0 + 68.36111111 -13.22222222x + x2 = 0 + 68.36111111 Combine like terms: 0 + 68.36111111 = 68.36111111 -13.22222222x + x2 = 68.36111111 The x term is -13.22222222x. Take half its coefficient (-6.61111111). Square it (43.70679011) and add it to both sides. Add '43.70679011' to each side of the equation. -13.22222222x + 43.70679011 + x2 = 68.36111111 + 43.70679011 Reorder the terms: 43.70679011 + -13.22222222x + x2 = 68.36111111 + 43.70679011 Combine like terms: 68.36111111 + 43.70679011 = 112.06790122 43.70679011 + -13.22222222x + x2 = 112.06790122 Factor a perfect square on the left side: (x + -6.61111111)(x + -6.61111111) = 112.06790122 Calculate the square root of the right side: 10.586212789 Break this problem into two subproblems by setting (x + -6.61111111) equal to 10.586212789 and -10.586212789.Subproblem 1
x + -6.61111111 = 10.586212789 Simplifying x + -6.61111111 = 10.586212789 Reorder the terms: -6.61111111 + x = 10.586212789 Solving -6.61111111 + x = 10.586212789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.61111111' to each side of the equation. -6.61111111 + 6.61111111 + x = 10.586212789 + 6.61111111 Combine like terms: -6.61111111 + 6.61111111 = 0.00000000 0.00000000 + x = 10.586212789 + 6.61111111 x = 10.586212789 + 6.61111111 Combine like terms: 10.586212789 + 6.61111111 = 17.197323899 x = 17.197323899 Simplifying x = 17.197323899Subproblem 2
x + -6.61111111 = -10.586212789 Simplifying x + -6.61111111 = -10.586212789 Reorder the terms: -6.61111111 + x = -10.586212789 Solving -6.61111111 + x = -10.586212789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.61111111' to each side of the equation. -6.61111111 + 6.61111111 + x = -10.586212789 + 6.61111111 Combine like terms: -6.61111111 + 6.61111111 = 0.00000000 0.00000000 + x = -10.586212789 + 6.61111111 x = -10.586212789 + 6.61111111 Combine like terms: -10.586212789 + 6.61111111 = -3.975101679 x = -3.975101679 Simplifying x = -3.975101679Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.197323899, -3.975101679}
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