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Simplifying x2 + 1210x = 435600 Reorder the terms: 1210x + x2 = 435600 Solving 1210x + x2 = 435600 Solving for variable 'x'. Reorder the terms: -435600 + 1210x + x2 = 435600 + -435600 Combine like terms: 435600 + -435600 = 0 -435600 + 1210x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '435600' to each side of the equation. -435600 + 1210x + 435600 + x2 = 0 + 435600 Reorder the terms: -435600 + 435600 + 1210x + x2 = 0 + 435600 Combine like terms: -435600 + 435600 = 0 0 + 1210x + x2 = 0 + 435600 1210x + x2 = 0 + 435600 Combine like terms: 0 + 435600 = 435600 1210x + x2 = 435600 The x term is 1210x. Take half its coefficient (605). Square it (366025) and add it to both sides. Add '366025' to each side of the equation. 1210x + 366025 + x2 = 435600 + 366025 Reorder the terms: 366025 + 1210x + x2 = 435600 + 366025 Combine like terms: 435600 + 366025 = 801625 366025 + 1210x + x2 = 801625 Factor a perfect square on the left side: (x + 605)(x + 605) = 801625 Calculate the square root of the right side: 895.335132785 Break this problem into two subproblems by setting (x + 605) equal to 895.335132785 and -895.335132785.Subproblem 1
x + 605 = 895.335132785 Simplifying x + 605 = 895.335132785 Reorder the terms: 605 + x = 895.335132785 Solving 605 + x = 895.335132785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-605' to each side of the equation. 605 + -605 + x = 895.335132785 + -605 Combine like terms: 605 + -605 = 0 0 + x = 895.335132785 + -605 x = 895.335132785 + -605 Combine like terms: 895.335132785 + -605 = 290.335132785 x = 290.335132785 Simplifying x = 290.335132785Subproblem 2
x + 605 = -895.335132785 Simplifying x + 605 = -895.335132785 Reorder the terms: 605 + x = -895.335132785 Solving 605 + x = -895.335132785 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-605' to each side of the equation. 605 + -605 + x = -895.335132785 + -605 Combine like terms: 605 + -605 = 0 0 + x = -895.335132785 + -605 x = -895.335132785 + -605 Combine like terms: -895.335132785 + -605 = -1500.335132785 x = -1500.335132785 Simplifying x = -1500.335132785Solution
The solution to the problem is based on the solutions from the subproblems. x = {290.335132785, -1500.335132785}
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