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Simplifying 9y + -4y(y + 1) = 31 Reorder the terms: 9y + -4y(1 + y) = 31 9y + (1 * -4y + y * -4y) = 31 9y + (-4y + -4y2) = 31 Combine like terms: 9y + -4y = 5y 5y + -4y2 = 31 Solving 5y + -4y2 = 31 Solving for variable 'y'. Reorder the terms: -31 + 5y + -4y2 = 31 + -31 Combine like terms: 31 + -31 = 0 -31 + 5y + -4y2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 7.75 + -1.25y + y2 = 0 Move the constant term to the right: Add '-7.75' to each side of the equation. 7.75 + -1.25y + -7.75 + y2 = 0 + -7.75 Reorder the terms: 7.75 + -7.75 + -1.25y + y2 = 0 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + -1.25y + y2 = 0 + -7.75 -1.25y + y2 = 0 + -7.75 Combine like terms: 0 + -7.75 = -7.75 -1.25y + y2 = -7.75 The y term is -1.25y. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25y + 0.390625 + y2 = -7.75 + 0.390625 Reorder the terms: 0.390625 + -1.25y + y2 = -7.75 + 0.390625 Combine like terms: -7.75 + 0.390625 = -7.359375 0.390625 + -1.25y + y2 = -7.359375 Factor a perfect square on the left side: (y + -0.625)(y + -0.625) = -7.359375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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