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Simplifying x2 + 0.05x + -0.1 = 0 Reorder the terms: -0.1 + 0.05x + x2 = 0 Solving -0.1 + 0.05x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.05x + 0.1 + x2 = 0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.05x + x2 = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.05x + x2 = 0 + 0.1 0.05x + x2 = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 0.05x + x2 = 0.1 The x term is 0.05x. Take half its coefficient (0.025). Square it (0.000625) and add it to both sides. Add '0.000625' to each side of the equation. 0.05x + 0.000625 + x2 = 0.1 + 0.000625 Reorder the terms: 0.000625 + 0.05x + x2 = 0.1 + 0.000625 Combine like terms: 0.1 + 0.000625 = 0.100625 0.000625 + 0.05x + x2 = 0.100625 Factor a perfect square on the left side: (x + 0.025)(x + 0.025) = 0.100625 Calculate the square root of the right side: 0.317214439 Break this problem into two subproblems by setting (x + 0.025) equal to 0.317214439 and -0.317214439.Subproblem 1
x + 0.025 = 0.317214439 Simplifying x + 0.025 = 0.317214439 Reorder the terms: 0.025 + x = 0.317214439 Solving 0.025 + x = 0.317214439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.025' to each side of the equation. 0.025 + -0.025 + x = 0.317214439 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + x = 0.317214439 + -0.025 x = 0.317214439 + -0.025 Combine like terms: 0.317214439 + -0.025 = 0.292214439 x = 0.292214439 Simplifying x = 0.292214439Subproblem 2
x + 0.025 = -0.317214439 Simplifying x + 0.025 = -0.317214439 Reorder the terms: 0.025 + x = -0.317214439 Solving 0.025 + x = -0.317214439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.025' to each side of the equation. 0.025 + -0.025 + x = -0.317214439 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + x = -0.317214439 + -0.025 x = -0.317214439 + -0.025 Combine like terms: -0.317214439 + -0.025 = -0.342214439 x = -0.342214439 Simplifying x = -0.342214439Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.292214439, -0.342214439}
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