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Simplifying x2 + 810x = 3240 Reorder the terms: 810x + x2 = 3240 Solving 810x + x2 = 3240 Solving for variable 'x'. Reorder the terms: -3240 + 810x + x2 = 3240 + -3240 Combine like terms: 3240 + -3240 = 0 -3240 + 810x + x2 = 0 Begin completing the square. 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 = 167265 164025 + 810x + x2 = 167265 Factor a perfect square on the left side: (x + 405)(x + 405) = 167265 Calculate the square root of the right side: 408.98043963 Break this problem into two subproblems by setting (x + 405) equal to 408.98043963 and -408.98043963.Subproblem 1
x + 405 = 408.98043963 Simplifying x + 405 = 408.98043963 Reorder the terms: 405 + x = 408.98043963 Solving 405 + x = 408.98043963 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 = 408.98043963 + -405 Combine like terms: 405 + -405 = 0 0 + x = 408.98043963 + -405 x = 408.98043963 + -405 Combine like terms: 408.98043963 + -405 = 3.98043963 x = 3.98043963 Simplifying x = 3.98043963Subproblem 2
x + 405 = -408.98043963 Simplifying x + 405 = -408.98043963 Reorder the terms: 405 + x = -408.98043963 Solving 405 + x = -408.98043963 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 = -408.98043963 + -405 Combine like terms: 405 + -405 = 0 0 + x = -408.98043963 + -405 x = -408.98043963 + -405 Combine like terms: -408.98043963 + -405 = -813.98043963 x = -813.98043963 Simplifying x = -813.98043963Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.98043963, -813.98043963}
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