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Simplifying y(40 + -1y) = 500 (40 * y + -1y * y) = 500 (40y + -1y2) = 500 Solving 40y + -1y2 = 500 Solving for variable 'y'. Reorder the terms: -500 + 40y + -1y2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 40y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 500 + -40y + y2 = 0 Move the constant term to the right: Add '-500' to each side of the equation. 500 + -40y + -500 + y2 = 0 + -500 Reorder the terms: 500 + -500 + -40y + y2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -40y + y2 = 0 + -500 -40y + y2 = 0 + -500 Combine like terms: 0 + -500 = -500 -40y + y2 = -500 The y term is -40y. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40y + 400 + y2 = -500 + 400 Reorder the terms: 400 + -40y + y2 = -500 + 400 Combine like terms: -500 + 400 = -100 400 + -40y + y2 = -100 Factor a perfect square on the left side: (y + -20)(y + -20) = -100 Can't calculate square root of the right side. The solution to this equation could not be determined.
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