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Simplifying 810x + -1x2 = 3240 Solving 810x + -1x2 = 3240 Solving for variable 'x'. Reorder the terms: -3240 + 810x + -1x2 = 3240 + -3240 Combine like terms: 3240 + -3240 = 0 -3240 + 810x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3240 + -810x + x2 = 0 Move the constant term to the right: Add '-3240' to each side of the equation. 3240 + -810x + -3240 + x2 = 0 + -3240 Reorder the terms: 3240 + -3240 + -810x + x2 = 0 + -3240 Combine like terms: 3240 + -3240 = 0 0 + -810x + x2 = 0 + -3240 -810x + x2 = 0 + -3240 Combine like terms: 0 + -3240 = -3240 -810x + x2 = -3240 The x term is -810x. Take half its coefficient (-405). Square it (164025) and add it to both sides. Add '164025' to each side of the equation. -810x + 164025 + x2 = -3240 + 164025 Reorder the terms: 164025 + -810x + x2 = -3240 + 164025 Combine like terms: -3240 + 164025 = 160785 164025 + -810x + x2 = 160785 Factor a perfect square on the left side: (x + -405)(x + -405) = 160785 Calculate the square root of the right side: 400.980049379 Break this problem into two subproblems by setting (x + -405) equal to 400.980049379 and -400.980049379.Subproblem 1
x + -405 = 400.980049379 Simplifying x + -405 = 400.980049379 Reorder the terms: -405 + x = 400.980049379 Solving -405 + x = 400.980049379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '405' to each side of the equation. -405 + 405 + x = 400.980049379 + 405 Combine like terms: -405 + 405 = 0 0 + x = 400.980049379 + 405 x = 400.980049379 + 405 Combine like terms: 400.980049379 + 405 = 805.980049379 x = 805.980049379 Simplifying x = 805.980049379Subproblem 2
x + -405 = -400.980049379 Simplifying x + -405 = -400.980049379 Reorder the terms: -405 + x = -400.980049379 Solving -405 + x = -400.980049379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '405' to each side of the equation. -405 + 405 + x = -400.980049379 + 405 Combine like terms: -405 + 405 = 0 0 + x = -400.980049379 + 405 x = -400.980049379 + 405 Combine like terms: -400.980049379 + 405 = 4.019950621 x = 4.019950621 Simplifying x = 4.019950621Solution
The solution to the problem is based on the solutions from the subproblems. x = {805.980049379, 4.019950621}
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