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Simplifying 3000x2 + 6000x + -370.8 = 0 Reorder the terms: -370.8 + 6000x + 3000x2 = 0 Solving -370.8 + 6000x + 3000x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3000 the coefficient of the squared term: Divide each side by '3000'. -0.1236 + 2x + x2 = 0 Move the constant term to the right: Add '0.1236' to each side of the equation. -0.1236 + 2x + 0.1236 + x2 = 0 + 0.1236 Reorder the terms: -0.1236 + 0.1236 + 2x + x2 = 0 + 0.1236 Combine like terms: -0.1236 + 0.1236 = 0.0000 0.0000 + 2x + x2 = 0 + 0.1236 2x + x2 = 0 + 0.1236 Combine like terms: 0 + 0.1236 = 0.1236 2x + x2 = 0.1236 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.1236 + 1 Reorder the terms: 1 + 2x + x2 = 0.1236 + 1 Combine like terms: 0.1236 + 1 = 1.1236 1 + 2x + x2 = 1.1236 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.1236 Calculate the square root of the right side: 1.06 Break this problem into two subproblems by setting (x + 1) equal to 1.06 and -1.06.Subproblem 1
x + 1 = 1.06 Simplifying x + 1 = 1.06 Reorder the terms: 1 + x = 1.06 Solving 1 + x = 1.06 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.06 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.06 + -1 x = 1.06 + -1 Combine like terms: 1.06 + -1 = 0.06 x = 0.06 Simplifying x = 0.06Subproblem 2
x + 1 = -1.06 Simplifying x + 1 = -1.06 Reorder the terms: 1 + x = -1.06 Solving 1 + x = -1.06 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.06 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.06 + -1 x = -1.06 + -1 Combine like terms: -1.06 + -1 = -2.06 x = -2.06 Simplifying x = -2.06Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.06, -2.06}
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