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Simplifying 0.001x2 + -0.003x = 0.004 Reorder the terms: -0.003x + 0.001x2 = 0.004 Solving -0.003x + 0.001x2 = 0.004 Solving for variable 'x'. Reorder the terms: -0.004 + -0.003x + 0.001x2 = 0.004 + -0.004 Combine like terms: 0.004 + -0.004 = 0.000 -0.004 + -0.003x + 0.001x2 = 0.000 Begin completing the square. Divide all terms by 0.001 the coefficient of the squared term: Divide each side by '0.001'. -4 + -3x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -3x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -3x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x + x2 = 0 + 4 -3x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -3x + x2 = 4 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 4 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 4 + 2.25 Combine like terms: 4 + 2.25 = 6.25 2.25 + -3x + x2 = 6.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + -1.5) equal to 2.5 and -2.5.Subproblem 1
x + -1.5 = 2.5 Simplifying x + -1.5 = 2.5 Reorder the terms: -1.5 + x = 2.5 Solving -1.5 + x = 2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.5 + 1.5 x = 2.5 + 1.5 Combine like terms: 2.5 + 1.5 = 4 x = 4 Simplifying x = 4Subproblem 2
x + -1.5 = -2.5 Simplifying x + -1.5 = -2.5 Reorder the terms: -1.5 + x = -2.5 Solving -1.5 + x = -2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.5 + 1.5 x = -2.5 + 1.5 Combine like terms: -2.5 + 1.5 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -1}
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