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Simplifying 11105 + -286x + x2 = 0 Solving 11105 + -286x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11105' to each side of the equation. 11105 + -286x + -11105 + x2 = 0 + -11105 Reorder the terms: 11105 + -11105 + -286x + x2 = 0 + -11105 Combine like terms: 11105 + -11105 = 0 0 + -286x + x2 = 0 + -11105 -286x + x2 = 0 + -11105 Combine like terms: 0 + -11105 = -11105 -286x + x2 = -11105 The x term is -286x. Take half its coefficient (-143). Square it (20449) and add it to both sides. Add '20449' to each side of the equation. -286x + 20449 + x2 = -11105 + 20449 Reorder the terms: 20449 + -286x + x2 = -11105 + 20449 Combine like terms: -11105 + 20449 = 9344 20449 + -286x + x2 = 9344 Factor a perfect square on the left side: (x + -143)(x + -143) = 9344 Calculate the square root of the right side: 96.664367789 Break this problem into two subproblems by setting (x + -143) equal to 96.664367789 and -96.664367789.Subproblem 1
x + -143 = 96.664367789 Simplifying x + -143 = 96.664367789 Reorder the terms: -143 + x = 96.664367789 Solving -143 + x = 96.664367789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '143' to each side of the equation. -143 + 143 + x = 96.664367789 + 143 Combine like terms: -143 + 143 = 0 0 + x = 96.664367789 + 143 x = 96.664367789 + 143 Combine like terms: 96.664367789 + 143 = 239.664367789 x = 239.664367789 Simplifying x = 239.664367789Subproblem 2
x + -143 = -96.664367789 Simplifying x + -143 = -96.664367789 Reorder the terms: -143 + x = -96.664367789 Solving -143 + x = -96.664367789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '143' to each side of the equation. -143 + 143 + x = -96.664367789 + 143 Combine like terms: -143 + 143 = 0 0 + x = -96.664367789 + 143 x = -96.664367789 + 143 Combine like terms: -96.664367789 + 143 = 46.335632211 x = 46.335632211 Simplifying x = 46.335632211Solution
The solution to the problem is based on the solutions from the subproblems. x = {239.664367789, 46.335632211}
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