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Simplifying x2 + 6000x + -90000 = 0 Reorder the terms: -90000 + 6000x + x2 = 0 Solving -90000 + 6000x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '90000' to each side of the equation. -90000 + 6000x + 90000 + x2 = 0 + 90000 Reorder the terms: -90000 + 90000 + 6000x + x2 = 0 + 90000 Combine like terms: -90000 + 90000 = 0 0 + 6000x + x2 = 0 + 90000 6000x + x2 = 0 + 90000 Combine like terms: 0 + 90000 = 90000 6000x + x2 = 90000 The x term is 6000x. Take half its coefficient (3000). Square it (9000000) and add it to both sides. Add '9000000' to each side of the equation. 6000x + 9000000 + x2 = 90000 + 9000000 Reorder the terms: 9000000 + 6000x + x2 = 90000 + 9000000 Combine like terms: 90000 + 9000000 = 9090000 9000000 + 6000x + x2 = 9090000 Factor a perfect square on the left side: (x + 3000)(x + 3000) = 9090000 Calculate the square root of the right side: 3014.962686336 Break this problem into two subproblems by setting (x + 3000) equal to 3014.962686336 and -3014.962686336.Subproblem 1
x + 3000 = 3014.962686336 Simplifying x + 3000 = 3014.962686336 Reorder the terms: 3000 + x = 3014.962686336 Solving 3000 + x = 3014.962686336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3000' to each side of the equation. 3000 + -3000 + x = 3014.962686336 + -3000 Combine like terms: 3000 + -3000 = 0 0 + x = 3014.962686336 + -3000 x = 3014.962686336 + -3000 Combine like terms: 3014.962686336 + -3000 = 14.962686336 x = 14.962686336 Simplifying x = 14.962686336Subproblem 2
x + 3000 = -3014.962686336 Simplifying x + 3000 = -3014.962686336 Reorder the terms: 3000 + x = -3014.962686336 Solving 3000 + x = -3014.962686336 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3000' to each side of the equation. 3000 + -3000 + x = -3014.962686336 + -3000 Combine like terms: 3000 + -3000 = 0 0 + x = -3014.962686336 + -3000 x = -3014.962686336 + -3000 Combine like terms: -3014.962686336 + -3000 = -6014.962686336 x = -6014.962686336 Simplifying x = -6014.962686336Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.962686336, -6014.962686336}
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