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Simplifying 0.001 = x2 + 0.03x Reorder the terms: 0.001 = 0.03x + x2 Solving 0.001 = 0.03x + x2 Solving for variable 'x'. Reorder the terms: 0.001 + -0.03x + -1x2 = 0.03x + -0.03x + x2 + -1x2 Combine like terms: 0.03x + -0.03x = 0.00 0.001 + -0.03x + -1x2 = 0.00 + x2 + -1x2 0.001 + -0.03x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.001 + -0.03x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.001 + 0.03x + x2 = 0 Move the constant term to the right: Add '0.001' to each side of the equation. -0.001 + 0.03x + 0.001 + x2 = 0 + 0.001 Reorder the terms: -0.001 + 0.001 + 0.03x + x2 = 0 + 0.001 Combine like terms: -0.001 + 0.001 = 0.000 0.000 + 0.03x + x2 = 0 + 0.001 0.03x + x2 = 0 + 0.001 Combine like terms: 0 + 0.001 = 0.001 0.03x + x2 = 0.001 The x term is 0.03x. Take half its coefficient (0.015). Square it (0.000225) and add it to both sides. Add '0.000225' to each side of the equation. 0.03x + 0.000225 + x2 = 0.001 + 0.000225 Reorder the terms: 0.000225 + 0.03x + x2 = 0.001 + 0.000225 Combine like terms: 0.001 + 0.000225 = 0.001225 0.000225 + 0.03x + x2 = 0.001225 Factor a perfect square on the left side: (x + 0.015)(x + 0.015) = 0.001225 Calculate the square root of the right side: 0.035 Break this problem into two subproblems by setting (x + 0.015) equal to 0.035 and -0.035.Subproblem 1
x + 0.015 = 0.035 Simplifying x + 0.015 = 0.035 Reorder the terms: 0.015 + x = 0.035 Solving 0.015 + x = 0.035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.015' to each side of the equation. 0.015 + -0.015 + x = 0.035 + -0.015 Combine like terms: 0.015 + -0.015 = 0.000 0.000 + x = 0.035 + -0.015 x = 0.035 + -0.015 Combine like terms: 0.035 + -0.015 = 0.02 x = 0.02 Simplifying x = 0.02Subproblem 2
x + 0.015 = -0.035 Simplifying x + 0.015 = -0.035 Reorder the terms: 0.015 + x = -0.035 Solving 0.015 + x = -0.035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.015' to each side of the equation. 0.015 + -0.015 + x = -0.035 + -0.015 Combine like terms: 0.015 + -0.015 = 0.000 0.000 + x = -0.035 + -0.015 x = -0.035 + -0.015 Combine like terms: -0.035 + -0.015 = -0.05 x = -0.05 Simplifying x = -0.05Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.02, -0.05}
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