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Simplifying x2 + -0.1x + -0.02 = 0 Reorder the terms: -0.02 + -0.1x + x2 = 0 Solving -0.02 + -0.1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.02' to each side of the equation. -0.02 + -0.1x + 0.02 + x2 = 0 + 0.02 Reorder the terms: -0.02 + 0.02 + -0.1x + x2 = 0 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + -0.1x + x2 = 0 + 0.02 -0.1x + x2 = 0 + 0.02 Combine like terms: 0 + 0.02 = 0.02 -0.1x + x2 = 0.02 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 = 0.02 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = 0.02 + 0.0025 Combine like terms: 0.02 + 0.0025 = 0.0225 0.0025 + -0.1x + x2 = 0.0225 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = 0.0225 Calculate the square root of the right side: 0.15 Break this problem into two subproblems by setting (x + -0.05) equal to 0.15 and -0.15.Subproblem 1
x + -0.05 = 0.15 Simplifying x + -0.05 = 0.15 Reorder the terms: -0.05 + x = 0.15 Solving -0.05 + x = 0.15 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 = 0.15 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = 0.15 + 0.05 x = 0.15 + 0.05 Combine like terms: 0.15 + 0.05 = 0.2 x = 0.2 Simplifying x = 0.2Subproblem 2
x + -0.05 = -0.15 Simplifying x + -0.05 = -0.15 Reorder the terms: -0.05 + x = -0.15 Solving -0.05 + x = -0.15 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 = -0.15 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + x = -0.15 + 0.05 x = -0.15 + 0.05 Combine like terms: -0.15 + 0.05 = -0.1 x = -0.1 Simplifying x = -0.1Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2, -0.1}
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