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Simplifying x2 + 0.1x + -0.2 = 0 Reorder the terms: -0.2 + 0.1x + x2 = 0 Solving -0.2 + 0.1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.1x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.1x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.1x + x2 = 0 + 0.2 0.1x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.1x + x2 = 0.2 The x term is 0.1x. Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. 0.1x + 0.0025 + x2 = 0.2 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 0.2 + 0.0025 Combine like terms: 0.2 + 0.0025 = 0.2025 0.0025 + 0.1x + x2 = 0.2025 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 0.2025 Calculate the square root of the right side: 0.45 Break this problem into two subproblems by setting (x + 0.05) equal to 0.45 and -0.45.Subproblem 1
x + 0.05 = 0.45 Simplifying x + 0.05 = 0.45 Reorder the terms: 0.05 + x = 0.45 Solving 0.05 + x = 0.45 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = 0.45 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.45 + -0.05 x = 0.45 + -0.05 Combine like terms: 0.45 + -0.05 = 0.4 x = 0.4 Simplifying x = 0.4Subproblem 2
x + 0.05 = -0.45 Simplifying x + 0.05 = -0.45 Reorder the terms: 0.05 + x = -0.45 Solving 0.05 + x = -0.45 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = -0.45 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.45 + -0.05 x = -0.45 + -0.05 Combine like terms: -0.45 + -0.05 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4, -0.5}
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