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Simplifying 100x + -0.1x2 = 50x + 10000 Reorder the terms: 100x + -0.1x2 = 10000 + 50x Solving 100x + -0.1x2 = 10000 + 50x Solving for variable 'x'. Reorder the terms: -10000 + 100x + -50x + -0.1x2 = 10000 + 50x + -10000 + -50x Combine like terms: 100x + -50x = 50x -10000 + 50x + -0.1x2 = 10000 + 50x + -10000 + -50x Reorder the terms: -10000 + 50x + -0.1x2 = 10000 + -10000 + 50x + -50x Combine like terms: 10000 + -10000 = 0 -10000 + 50x + -0.1x2 = 0 + 50x + -50x -10000 + 50x + -0.1x2 = 50x + -50x Combine like terms: 50x + -50x = 0 -10000 + 50x + -0.1x2 = 0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 100000 + -500x + x2 = 0 Move the constant term to the right: Add '-100000' to each side of the equation. 100000 + -500x + -100000 + x2 = 0 + -100000 Reorder the terms: 100000 + -100000 + -500x + x2 = 0 + -100000 Combine like terms: 100000 + -100000 = 0 0 + -500x + x2 = 0 + -100000 -500x + x2 = 0 + -100000 Combine like terms: 0 + -100000 = -100000 -500x + x2 = -100000 The x term is -500x. Take half its coefficient (-250). Square it (62500) and add it to both sides. Add '62500' to each side of the equation. -500x + 62500 + x2 = -100000 + 62500 Reorder the terms: 62500 + -500x + x2 = -100000 + 62500 Combine like terms: -100000 + 62500 = -37500 62500 + -500x + x2 = -37500 Factor a perfect square on the left side: (x + -250)(x + -250) = -37500 Can't calculate square root of the right side. The solution to this equation could not be determined.
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