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Simplifying 2(4y + -5) + -1(3y + 6) = 2y(y + 3) Reorder the terms: 2(-5 + 4y) + -1(3y + 6) = 2y(y + 3) (-5 * 2 + 4y * 2) + -1(3y + 6) = 2y(y + 3) (-10 + 8y) + -1(3y + 6) = 2y(y + 3) Reorder the terms: -10 + 8y + -1(6 + 3y) = 2y(y + 3) -10 + 8y + (6 * -1 + 3y * -1) = 2y(y + 3) -10 + 8y + (-6 + -3y) = 2y(y + 3) Reorder the terms: -10 + -6 + 8y + -3y = 2y(y + 3) Combine like terms: -10 + -6 = -16 -16 + 8y + -3y = 2y(y + 3) Combine like terms: 8y + -3y = 5y -16 + 5y = 2y(y + 3) Reorder the terms: -16 + 5y = 2y(3 + y) -16 + 5y = (3 * 2y + y * 2y) -16 + 5y = (6y + 2y2) Solving -16 + 5y = 6y + 2y2 Solving for variable 'y'. Combine like terms: 5y + -6y = -1y -16 + -1y + -2y2 = 6y + 2y2 + -6y + -2y2 Reorder the terms: -16 + -1y + -2y2 = 6y + -6y + 2y2 + -2y2 Combine like terms: 6y + -6y = 0 -16 + -1y + -2y2 = 0 + 2y2 + -2y2 -16 + -1y + -2y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 -16 + -1y + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + y + 2y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + y + 2y2)' equal to zero and attempt to solve: Simplifying 16 + y + 2y2 = 0 Solving 16 + y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8 + 0.5y + y2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 0.5y + -8 + y2 = 0 + -8 Reorder the terms: 8 + -8 + 0.5y + y2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 0.5y + y2 = 0 + -8 0.5y + y2 = 0 + -8 Combine like terms: 0 + -8 = -8 0.5y + y2 = -8 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5y + 0.25 + y2 = -8 + 0.25 Reorder the terms: 0.25 + 0.5y + y2 = -8 + 0.25 Combine like terms: -8 + 0.25 = -7.75 0.25 + 0.5y + y2 = -7.75 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -7.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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