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Simplifying 3x2 + 12x = 1000 Reorder the terms: 12x + 3x2 = 1000 Solving 12x + 3x2 = 1000 Solving for variable 'x'. Reorder the terms: -1000 + 12x + 3x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + 12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -333.3333333 + 4x + x2 = 0 Move the constant term to the right: Add '333.3333333' to each side of the equation. -333.3333333 + 4x + 333.3333333 + x2 = 0 + 333.3333333 Reorder the terms: -333.3333333 + 333.3333333 + 4x + x2 = 0 + 333.3333333 Combine like terms: -333.3333333 + 333.3333333 = 0.0000000 0.0000000 + 4x + x2 = 0 + 333.3333333 4x + x2 = 0 + 333.3333333 Combine like terms: 0 + 333.3333333 = 333.3333333 4x + x2 = 333.3333333 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 333.3333333 + 4 Reorder the terms: 4 + 4x + x2 = 333.3333333 + 4 Combine like terms: 333.3333333 + 4 = 337.3333333 4 + 4x + x2 = 337.3333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 337.3333333 Calculate the square root of the right side: 18.366636418 Break this problem into two subproblems by setting (x + 2) equal to 18.366636418 and -18.366636418.Subproblem 1
x + 2 = 18.366636418 Simplifying x + 2 = 18.366636418 Reorder the terms: 2 + x = 18.366636418 Solving 2 + x = 18.366636418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 18.366636418 + -2 Combine like terms: 2 + -2 = 0 0 + x = 18.366636418 + -2 x = 18.366636418 + -2 Combine like terms: 18.366636418 + -2 = 16.366636418 x = 16.366636418 Simplifying x = 16.366636418Subproblem 2
x + 2 = -18.366636418 Simplifying x + 2 = -18.366636418 Reorder the terms: 2 + x = -18.366636418 Solving 2 + x = -18.366636418 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -18.366636418 + -2 Combine like terms: 2 + -2 = 0 0 + x = -18.366636418 + -2 x = -18.366636418 + -2 Combine like terms: -18.366636418 + -2 = -20.366636418 x = -20.366636418 Simplifying x = -20.366636418Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.366636418, -20.366636418}
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