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Simplifying 0.2x2 + -80x + 10000 = x Reorder the terms: 10000 + -80x + 0.2x2 = x Solving 10000 + -80x + 0.2x2 = x Solving for variable 'x'. Reorder the terms: 10000 + -80x + -1x + 0.2x2 = x + -1x Combine like terms: -80x + -1x = -81x 10000 + -81x + 0.2x2 = x + -1x Combine like terms: x + -1x = 0 10000 + -81x + 0.2x2 = 0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 50000 + -405x + x2 = 0 Move the constant term to the right: Add '-50000' to each side of the equation. 50000 + -405x + -50000 + x2 = 0 + -50000 Reorder the terms: 50000 + -50000 + -405x + x2 = 0 + -50000 Combine like terms: 50000 + -50000 = 0 0 + -405x + x2 = 0 + -50000 -405x + x2 = 0 + -50000 Combine like terms: 0 + -50000 = -50000 -405x + x2 = -50000 The x term is -405x. Take half its coefficient (-202.5). Square it (41006.25) and add it to both sides. Add '41006.25' to each side of the equation. -405x + 41006.25 + x2 = -50000 + 41006.25 Reorder the terms: 41006.25 + -405x + x2 = -50000 + 41006.25 Combine like terms: -50000 + 41006.25 = -8993.75 41006.25 + -405x + x2 = -8993.75 Factor a perfect square on the left side: (x + -202.5)(x + -202.5) = -8993.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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