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Simplifying 0 = x2 + 6000x + -12000 Reorder the terms: 0 = -12000 + 6000x + x2 Solving 0 = -12000 + 6000x + x2 Solving for variable 'x'. Combine like terms: 0 + 12000 = 12000 12000 + -6000x + -1x2 = -12000 + 6000x + x2 + 12000 + -6000x + -1x2 Reorder the terms: 12000 + -6000x + -1x2 = -12000 + 12000 + 6000x + -6000x + x2 + -1x2 Combine like terms: -12000 + 12000 = 0 12000 + -6000x + -1x2 = 0 + 6000x + -6000x + x2 + -1x2 12000 + -6000x + -1x2 = 6000x + -6000x + x2 + -1x2 Combine like terms: 6000x + -6000x = 0 12000 + -6000x + -1x2 = 0 + x2 + -1x2 12000 + -6000x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 12000 + -6000x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12000 + 6000x + x2 = 0 Move the constant term to the right: Add '12000' to each side of the equation. -12000 + 6000x + 12000 + x2 = 0 + 12000 Reorder the terms: -12000 + 12000 + 6000x + x2 = 0 + 12000 Combine like terms: -12000 + 12000 = 0 0 + 6000x + x2 = 0 + 12000 6000x + x2 = 0 + 12000 Combine like terms: 0 + 12000 = 12000 6000x + x2 = 12000 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 = 12000 + 9000000 Reorder the terms: 9000000 + 6000x + x2 = 12000 + 9000000 Combine like terms: 12000 + 9000000 = 9012000 9000000 + 6000x + x2 = 9012000 Factor a perfect square on the left side: (x + 3000)(x + 3000) = 9012000 Calculate the square root of the right side: 3001.999333777 Break this problem into two subproblems by setting (x + 3000) equal to 3001.999333777 and -3001.999333777.Subproblem 1
x + 3000 = 3001.999333777 Simplifying x + 3000 = 3001.999333777 Reorder the terms: 3000 + x = 3001.999333777 Solving 3000 + x = 3001.999333777 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 = 3001.999333777 + -3000 Combine like terms: 3000 + -3000 = 0 0 + x = 3001.999333777 + -3000 x = 3001.999333777 + -3000 Combine like terms: 3001.999333777 + -3000 = 1.999333777 x = 1.999333777 Simplifying x = 1.999333777Subproblem 2
x + 3000 = -3001.999333777 Simplifying x + 3000 = -3001.999333777 Reorder the terms: 3000 + x = -3001.999333777 Solving 3000 + x = -3001.999333777 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 = -3001.999333777 + -3000 Combine like terms: 3000 + -3000 = 0 0 + x = -3001.999333777 + -3000 x = -3001.999333777 + -3000 Combine like terms: -3001.999333777 + -3000 = -6001.999333777 x = -6001.999333777 Simplifying x = -6001.999333777Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.999333777, -6001.999333777}
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