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Simplifying x2 + (0.045 + 0.00265 + 0.00276) * x + (-0.01482 * 0.045 + 0.00265 * 0.00276) = 0 Combine like terms: 0.045 + 0.00265 = 0.04765 x2 + (0.04765 + 0.00276) * x + (-0.01482 * 0.045 + 0.00265 * 0.00276) = 0 Combine like terms: 0.04765 + 0.00276 = 0.05041 x2 + (0.05041) * x + (-0.01482 * 0.045 + 0.00265 * 0.00276) = 0 Multiply -0.01482 * 0.045 x2 + 0.05041x + (-0.0006669 + 0.00265 * 0.00276) = 0 Multiply 0.00265 * 0.00276 x2 + 0.05041x + (-0.0006669 + 0.000007314) = 0 Combine like terms: -0.0006669 + 0.000007314 = -0.000659586 x2 + 0.05041x + (-0.000659586) = 0 x2 + 0.05041x + -0.000659586 = 0 Reorder the terms: -0.000659586 + 0.05041x + x2 = 0 Solving -0.000659586 + 0.05041x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.000659586' to each side of the equation. -0.000659586 + 0.05041x + 0.000659586 + x2 = 0 + 0.000659586 Reorder the terms: -0.000659586 + 0.000659586 + 0.05041x + x2 = 0 + 0.000659586 Combine like terms: -0.000659586 + 0.000659586 = 0.000000000 0.000000000 + 0.05041x + x2 = 0 + 0.000659586 0.05041x + x2 = 0 + 0.000659586 Combine like terms: 0 + 0.000659586 = 0.000659586 0.05041x + x2 = 0.000659586 The x term is 0.05041x. Take half its coefficient (0.025205). Square it (0.000635292025) and add it to both sides. Add '0.000635292025' to each side of the equation. 0.05041x + 0.000635292025 + x2 = 0.000659586 + 0.000635292025 Reorder the terms: 0.000635292025 + 0.05041x + x2 = 0.000659586 + 0.000635292025 Combine like terms: 0.000659586 + 0.000635292025 = 0.001294878025 0.000635292025 + 0.05041x + x2 = 0.001294878025 Factor a perfect square on the left side: (x + 0.025205)(x + 0.025205) = 0.001294878025 Calculate the square root of the right side: 0.035984414 Break this problem into two subproblems by setting (x + 0.025205) equal to 0.035984414 and -0.035984414.Subproblem 1
x + 0.025205 = 0.035984414 Simplifying x + 0.025205 = 0.035984414 Reorder the terms: 0.025205 + x = 0.035984414 Solving 0.025205 + x = 0.035984414 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.025205' to each side of the equation. 0.025205 + -0.025205 + x = 0.035984414 + -0.025205 Combine like terms: 0.025205 + -0.025205 = 0.000000 0.000000 + x = 0.035984414 + -0.025205 x = 0.035984414 + -0.025205 Combine like terms: 0.035984414 + -0.025205 = 0.010779414 x = 0.010779414 Simplifying x = 0.010779414Subproblem 2
x + 0.025205 = -0.035984414 Simplifying x + 0.025205 = -0.035984414 Reorder the terms: 0.025205 + x = -0.035984414 Solving 0.025205 + x = -0.035984414 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.025205' to each side of the equation. 0.025205 + -0.025205 + x = -0.035984414 + -0.025205 Combine like terms: 0.025205 + -0.025205 = 0.000000 0.000000 + x = -0.035984414 + -0.025205 x = -0.035984414 + -0.025205 Combine like terms: -0.035984414 + -0.025205 = -0.061189414 x = -0.061189414 Simplifying x = -0.061189414Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.010779414, -0.061189414}
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