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Simplifying 51 = -1y2 + 4y Reorder the terms: 51 = 4y + -1y2 Solving 51 = 4y + -1y2 Solving for variable 'y'. Reorder the terms: 51 + -4y + y2 = 4y + -4y + -1y2 + y2 Combine like terms: 4y + -4y = 0 51 + -4y + y2 = 0 + -1y2 + y2 51 + -4y + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 51 + -4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-51' to each side of the equation. 51 + -4y + -51 + y2 = 0 + -51 Reorder the terms: 51 + -51 + -4y + y2 = 0 + -51 Combine like terms: 51 + -51 = 0 0 + -4y + y2 = 0 + -51 -4y + y2 = 0 + -51 Combine like terms: 0 + -51 = -51 -4y + y2 = -51 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = -51 + 4 Reorder the terms: 4 + -4y + y2 = -51 + 4 Combine like terms: -51 + 4 = -47 4 + -4y + y2 = -47 Factor a perfect square on the left side: (y + -2)(y + -2) = -47 Can't calculate square root of the right side. The solution to this equation could not be determined.
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