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Simplifying 6x + -0.025x2 = 500 + x Solving 6x + -0.025x2 = 500 + x Solving for variable 'x'. Reorder the terms: -500 + 6x + -1x + -0.025x2 = 500 + x + -500 + -1x Combine like terms: 6x + -1x = 5x -500 + 5x + -0.025x2 = 500 + x + -500 + -1x Reorder the terms: -500 + 5x + -0.025x2 = 500 + -500 + x + -1x Combine like terms: 500 + -500 = 0 -500 + 5x + -0.025x2 = 0 + x + -1x -500 + 5x + -0.025x2 = x + -1x Combine like terms: x + -1x = 0 -500 + 5x + -0.025x2 = 0 Begin completing the square. Divide all terms by -0.025 the coefficient of the squared term: Divide each side by '-0.025'. 20000 + -200x + x2 = 0 Move the constant term to the right: Add '-20000' to each side of the equation. 20000 + -200x + -20000 + x2 = 0 + -20000 Reorder the terms: 20000 + -20000 + -200x + x2 = 0 + -20000 Combine like terms: 20000 + -20000 = 0 0 + -200x + x2 = 0 + -20000 -200x + x2 = 0 + -20000 Combine like terms: 0 + -20000 = -20000 -200x + x2 = -20000 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -20000 + 10000 Reorder the terms: 10000 + -200x + x2 = -20000 + 10000 Combine like terms: -20000 + 10000 = -10000 10000 + -200x + x2 = -10000 Factor a perfect square on the left side: (x + -100)(x + -100) = -10000 Can't calculate square root of the right side. The solution to this equation could not be determined.
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