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Simplifying 0.28 = x(0.25(1 + -1x)) 0.28 = x((1 * 0.25 + -1x * 0.25)) 0.28 = x((0.25 + -0.25x)) 0.28 = (0.25 * x + -0.25x * x) 0.28 = (0.25x + -0.25x2) Solving 0.28 = 0.25x + -0.25x2 Solving for variable 'x'. Reorder the terms: 0.28 + -0.25x + 0.25x2 = 0.25x + -0.25x + -0.25x2 + 0.25x2 Combine like terms: 0.25x + -0.25x = 0.00 0.28 + -0.25x + 0.25x2 = 0.00 + -0.25x2 + 0.25x2 0.28 + -0.25x + 0.25x2 = -0.25x2 + 0.25x2 Combine like terms: -0.25x2 + 0.25x2 = 0.00 0.28 + -0.25x + 0.25x2 = 0.00 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 1.12 + -1x + x2 = 0 Move the constant term to the right: Add '-1.12' to each side of the equation. 1.12 + -1x + -1.12 + x2 = 0 + -1.12 Reorder the terms: 1.12 + -1.12 + -1x + x2 = 0 + -1.12 Combine like terms: 1.12 + -1.12 = 0.00 0.00 + -1x + x2 = 0 + -1.12 -1x + x2 = 0 + -1.12 Combine like terms: 0 + -1.12 = -1.12 -1x + x2 = -1.12 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -1.12 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -1.12 + 0.25 Combine like terms: -1.12 + 0.25 = -0.87 0.25 + -1x + x2 = -0.87 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -0.87 Can't calculate square root of the right side. The solution to this equation could not be determined.
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