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Simplifying x2 + 0.05x + -0.6 = 0 Reorder the terms: -0.6 + 0.05x + x2 = 0 Solving -0.6 + 0.05x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 0.05x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 0.05x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 0.05x + x2 = 0 + 0.6 0.05x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 0.05x + x2 = 0.6 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 = 0.6 + 0.000625 Reorder the terms: 0.000625 + 0.05x + x2 = 0.6 + 0.000625 Combine like terms: 0.6 + 0.000625 = 0.600625 0.000625 + 0.05x + x2 = 0.600625 Factor a perfect square on the left side: (x + 0.025)(x + 0.025) = 0.600625 Calculate the square root of the right side: 0.775 Break this problem into two subproblems by setting (x + 0.025) equal to 0.775 and -0.775.Subproblem 1
x + 0.025 = 0.775 Simplifying x + 0.025 = 0.775 Reorder the terms: 0.025 + x = 0.775 Solving 0.025 + x = 0.775 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 = 0.775 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + x = 0.775 + -0.025 x = 0.775 + -0.025 Combine like terms: 0.775 + -0.025 = 0.75 x = 0.75 Simplifying x = 0.75Subproblem 2
x + 0.025 = -0.775 Simplifying x + 0.025 = -0.775 Reorder the terms: 0.025 + x = -0.775 Solving 0.025 + x = -0.775 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 = -0.775 + -0.025 Combine like terms: 0.025 + -0.025 = 0.000 0.000 + x = -0.775 + -0.025 x = -0.775 + -0.025 Combine like terms: -0.775 + -0.025 = -0.8 x = -0.8 Simplifying x = -0.8Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.75, -0.8}
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