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Simplifying x2 + 600x + -2880000 = 0 Reorder the terms: -2880000 + 600x + x2 = 0 Solving -2880000 + 600x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2880000' to each side of the equation. -2880000 + 600x + 2880000 + x2 = 0 + 2880000 Reorder the terms: -2880000 + 2880000 + 600x + x2 = 0 + 2880000 Combine like terms: -2880000 + 2880000 = 0 0 + 600x + x2 = 0 + 2880000 600x + x2 = 0 + 2880000 Combine like terms: 0 + 2880000 = 2880000 600x + x2 = 2880000 The x term is 600x. Take half its coefficient (300). Square it (90000) and add it to both sides. Add '90000' to each side of the equation. 600x + 90000 + x2 = 2880000 + 90000 Reorder the terms: 90000 + 600x + x2 = 2880000 + 90000 Combine like terms: 2880000 + 90000 = 2970000 90000 + 600x + x2 = 2970000 Factor a perfect square on the left side: (x + 300)(x + 300) = 2970000 Calculate the square root of the right side: 1723.368793961 Break this problem into two subproblems by setting (x + 300) equal to 1723.368793961 and -1723.368793961.Subproblem 1
x + 300 = 1723.368793961 Simplifying x + 300 = 1723.368793961 Reorder the terms: 300 + x = 1723.368793961 Solving 300 + x = 1723.368793961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = 1723.368793961 + -300 Combine like terms: 300 + -300 = 0 0 + x = 1723.368793961 + -300 x = 1723.368793961 + -300 Combine like terms: 1723.368793961 + -300 = 1423.368793961 x = 1423.368793961 Simplifying x = 1423.368793961Subproblem 2
x + 300 = -1723.368793961 Simplifying x + 300 = -1723.368793961 Reorder the terms: 300 + x = -1723.368793961 Solving 300 + x = -1723.368793961 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = -1723.368793961 + -300 Combine like terms: 300 + -300 = 0 0 + x = -1723.368793961 + -300 x = -1723.368793961 + -300 Combine like terms: -1723.368793961 + -300 = -2023.368793961 x = -2023.368793961 Simplifying x = -2023.368793961Solution
The solution to the problem is based on the solutions from the subproblems. x = {1423.368793961, -2023.368793961}
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