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Simplifying 0.4 = x(0.01 + -1x) 0.4 = (0.01 * x + -1x * x) 0.4 = (0.01x + -1x2) Solving 0.4 = 0.01x + -1x2 Solving for variable 'x'. Reorder the terms: 0.4 + -0.01x + x2 = 0.01x + -0.01x + -1x2 + x2 Combine like terms: 0.01x + -0.01x = 0.00 0.4 + -0.01x + x2 = 0.00 + -1x2 + x2 0.4 + -0.01x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 0.4 + -0.01x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -0.01x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -0.01x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -0.01x + x2 = 0 + -0.4 -0.01x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -0.01x + x2 = -0.4 The x term is -0.01x. Take half its coefficient (-0.005). Square it (0.000025) and add it to both sides. Add '0.000025' to each side of the equation. -0.01x + 0.000025 + x2 = -0.4 + 0.000025 Reorder the terms: 0.000025 + -0.01x + x2 = -0.4 + 0.000025 Combine like terms: -0.4 + 0.000025 = -0.399975 0.000025 + -0.01x + x2 = -0.399975 Factor a perfect square on the left side: (x + -0.005)(x + -0.005) = -0.399975 Can't calculate square root of the right side. The solution to this equation could not be determined.
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