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Simplifying 50(x) = -0.4x2 + 80x + -1600 Reorder the terms: 50x = -1600 + 80x + -0.4x2 Solving 50x = -1600 + 80x + -0.4x2 Solving for variable 'x'. Reorder the terms: 1600 + 50x + -80x + 0.4x2 = -1600 + 80x + -0.4x2 + 1600 + -80x + 0.4x2 Combine like terms: 50x + -80x = -30x 1600 + -30x + 0.4x2 = -1600 + 80x + -0.4x2 + 1600 + -80x + 0.4x2 Reorder the terms: 1600 + -30x + 0.4x2 = -1600 + 1600 + 80x + -80x + -0.4x2 + 0.4x2 Combine like terms: -1600 + 1600 = 0 1600 + -30x + 0.4x2 = 0 + 80x + -80x + -0.4x2 + 0.4x2 1600 + -30x + 0.4x2 = 80x + -80x + -0.4x2 + 0.4x2 Combine like terms: 80x + -80x = 0 1600 + -30x + 0.4x2 = 0 + -0.4x2 + 0.4x2 1600 + -30x + 0.4x2 = -0.4x2 + 0.4x2 Combine like terms: -0.4x2 + 0.4x2 = 0.0 1600 + -30x + 0.4x2 = 0.0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 4000 + -75x + x2 = 0 Move the constant term to the right: Add '-4000' to each side of the equation. 4000 + -75x + -4000 + x2 = 0 + -4000 Reorder the terms: 4000 + -4000 + -75x + x2 = 0 + -4000 Combine like terms: 4000 + -4000 = 0 0 + -75x + x2 = 0 + -4000 -75x + x2 = 0 + -4000 Combine like terms: 0 + -4000 = -4000 -75x + x2 = -4000 The x term is -75x. Take half its coefficient (-37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. -75x + 1406.25 + x2 = -4000 + 1406.25 Reorder the terms: 1406.25 + -75x + x2 = -4000 + 1406.25 Combine like terms: -4000 + 1406.25 = -2593.75 1406.25 + -75x + x2 = -2593.75 Factor a perfect square on the left side: (x + -37.5)(x + -37.5) = -2593.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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