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Simplifying 0.169 + -0.169x = x2 Solving 0.169 + -0.169x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 0.169 + -0.169x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.169 + 0.169x + x2 = 0 Move the constant term to the right: Add '0.169' to each side of the equation. -0.169 + 0.169x + 0.169 + x2 = 0 + 0.169 Reorder the terms: -0.169 + 0.169 + 0.169x + x2 = 0 + 0.169 Combine like terms: -0.169 + 0.169 = 0.000 0.000 + 0.169x + x2 = 0 + 0.169 0.169x + x2 = 0 + 0.169 Combine like terms: 0 + 0.169 = 0.169 0.169x + x2 = 0.169 The x term is 0.169x. Take half its coefficient (0.0845). Square it (0.00714025) and add it to both sides. Add '0.00714025' to each side of the equation. 0.169x + 0.00714025 + x2 = 0.169 + 0.00714025 Reorder the terms: 0.00714025 + 0.169x + x2 = 0.169 + 0.00714025 Combine like terms: 0.169 + 0.00714025 = 0.17614025 0.00714025 + 0.169x + x2 = 0.17614025 Factor a perfect square on the left side: (x + 0.0845)(x + 0.0845) = 0.17614025 Calculate the square root of the right side: 0.41969066 Break this problem into two subproblems by setting (x + 0.0845) equal to 0.41969066 and -0.41969066.Subproblem 1
x + 0.0845 = 0.41969066 Simplifying x + 0.0845 = 0.41969066 Reorder the terms: 0.0845 + x = 0.41969066 Solving 0.0845 + x = 0.41969066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0845' to each side of the equation. 0.0845 + -0.0845 + x = 0.41969066 + -0.0845 Combine like terms: 0.0845 + -0.0845 = 0.0000 0.0000 + x = 0.41969066 + -0.0845 x = 0.41969066 + -0.0845 Combine like terms: 0.41969066 + -0.0845 = 0.33519066 x = 0.33519066 Simplifying x = 0.33519066Subproblem 2
x + 0.0845 = -0.41969066 Simplifying x + 0.0845 = -0.41969066 Reorder the terms: 0.0845 + x = -0.41969066 Solving 0.0845 + x = -0.41969066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0845' to each side of the equation. 0.0845 + -0.0845 + x = -0.41969066 + -0.0845 Combine like terms: 0.0845 + -0.0845 = 0.0000 0.0000 + x = -0.41969066 + -0.0845 x = -0.41969066 + -0.0845 Combine like terms: -0.41969066 + -0.0845 = -0.50419066 x = -0.50419066 Simplifying x = -0.50419066Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.33519066, -0.50419066}
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