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Simplifying 0 = (x2) + 0.005x + -0.0005 0 = x2 + 0.005x + -0.0005 Reorder the terms: 0 = -0.0005 + 0.005x + x2 Solving 0 = -0.0005 + 0.005x + x2 Solving for variable 'x'. Combine like terms: 0 + 0.0005 = 0.0005 0.0005 + -0.005x + -1x2 = -0.0005 + 0.005x + x2 + 0.0005 + -0.005x + -1x2 Reorder the terms: 0.0005 + -0.005x + -1x2 = -0.0005 + 0.0005 + 0.005x + -0.005x + x2 + -1x2 Combine like terms: -0.0005 + 0.0005 = 0.0000 0.0005 + -0.005x + -1x2 = 0.0000 + 0.005x + -0.005x + x2 + -1x2 0.0005 + -0.005x + -1x2 = 0.005x + -0.005x + x2 + -1x2 Combine like terms: 0.005x + -0.005x = 0.000 0.0005 + -0.005x + -1x2 = 0.000 + x2 + -1x2 0.0005 + -0.005x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 0.0005 + -0.005x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.0005 + 0.005x + x2 = 0 Move the constant term to the right: Add '0.0005' to each side of the equation. -0.0005 + 0.005x + 0.0005 + x2 = 0 + 0.0005 Reorder the terms: -0.0005 + 0.0005 + 0.005x + x2 = 0 + 0.0005 Combine like terms: -0.0005 + 0.0005 = 0.0000 0.0000 + 0.005x + x2 = 0 + 0.0005 0.005x + x2 = 0 + 0.0005 Combine like terms: 0 + 0.0005 = 0.0005 0.005x + x2 = 0.0005 The x term is 0.005x. Take half its coefficient (0.0025). Square it (0.00000625) and add it to both sides. Add '0.00000625' to each side of the equation. 0.005x + 0.00000625 + x2 = 0.0005 + 0.00000625 Reorder the terms: 0.00000625 + 0.005x + x2 = 0.0005 + 0.00000625 Combine like terms: 0.0005 + 0.00000625 = 0.00050625 0.00000625 + 0.005x + x2 = 0.00050625 Factor a perfect square on the left side: (x + 0.0025)(x + 0.0025) = 0.00050625 Calculate the square root of the right side: 0.0225 Break this problem into two subproblems by setting (x + 0.0025) equal to 0.0225 and -0.0225.Subproblem 1
x + 0.0025 = 0.0225 Simplifying x + 0.0025 = 0.0225 Reorder the terms: 0.0025 + x = 0.0225 Solving 0.0025 + x = 0.0225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0025' to each side of the equation. 0.0025 + -0.0025 + x = 0.0225 + -0.0025 Combine like terms: 0.0025 + -0.0025 = 0.0000 0.0000 + x = 0.0225 + -0.0025 x = 0.0225 + -0.0025 Combine like terms: 0.0225 + -0.0025 = 0.02 x = 0.02 Simplifying x = 0.02Subproblem 2
x + 0.0025 = -0.0225 Simplifying x + 0.0025 = -0.0225 Reorder the terms: 0.0025 + x = -0.0225 Solving 0.0025 + x = -0.0225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0025' to each side of the equation. 0.0025 + -0.0025 + x = -0.0225 + -0.0025 Combine like terms: 0.0025 + -0.0025 = 0.0000 0.0000 + x = -0.0225 + -0.0025 x = -0.0225 + -0.0025 Combine like terms: -0.0225 + -0.0025 = -0.025 x = -0.025 Simplifying x = -0.025Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.02, -0.025}
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