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Simplifying x2 + 4000x + -4000000 = 0 Reorder the terms: -4000000 + 4000x + x2 = 0 Solving -4000000 + 4000x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4000000' to each side of the equation. -4000000 + 4000x + 4000000 + x2 = 0 + 4000000 Reorder the terms: -4000000 + 4000000 + 4000x + x2 = 0 + 4000000 Combine like terms: -4000000 + 4000000 = 0 0 + 4000x + x2 = 0 + 4000000 4000x + x2 = 0 + 4000000 Combine like terms: 0 + 4000000 = 4000000 4000x + x2 = 4000000 The x term is 4000x. Take half its coefficient (2000). Square it (4000000) and add it to both sides. Add '4000000' to each side of the equation. 4000x + 4000000 + x2 = 4000000 + 4000000 Reorder the terms: 4000000 + 4000x + x2 = 4000000 + 4000000 Combine like terms: 4000000 + 4000000 = 8000000 4000000 + 4000x + x2 = 8000000 Factor a perfect square on the left side: (x + 2000)(x + 2000) = 8000000 Calculate the square root of the right side: 2828.427124746 Break this problem into two subproblems by setting (x + 2000) equal to 2828.427124746 and -2828.427124746.Subproblem 1
x + 2000 = 2828.427124746 Simplifying x + 2000 = 2828.427124746 Reorder the terms: 2000 + x = 2828.427124746 Solving 2000 + x = 2828.427124746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2000' to each side of the equation. 2000 + -2000 + x = 2828.427124746 + -2000 Combine like terms: 2000 + -2000 = 0 0 + x = 2828.427124746 + -2000 x = 2828.427124746 + -2000 Combine like terms: 2828.427124746 + -2000 = 828.427124746 x = 828.427124746 Simplifying x = 828.427124746Subproblem 2
x + 2000 = -2828.427124746 Simplifying x + 2000 = -2828.427124746 Reorder the terms: 2000 + x = -2828.427124746 Solving 2000 + x = -2828.427124746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2000' to each side of the equation. 2000 + -2000 + x = -2828.427124746 + -2000 Combine like terms: 2000 + -2000 = 0 0 + x = -2828.427124746 + -2000 x = -2828.427124746 + -2000 Combine like terms: -2828.427124746 + -2000 = -4828.427124746 x = -4828.427124746 Simplifying x = -4828.427124746Solution
The solution to the problem is based on the solutions from the subproblems. x = {828.427124746, -4828.427124746}
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