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Simplifying (-4y2 + -5y) + (2y2 + 2y + -2) = 0 Reorder the terms: (-5y + -4y2) + (2y2 + 2y + -2) = 0 Remove parenthesis around (-5y + -4y2) -5y + -4y2 + (2y2 + 2y + -2) = 0 Reorder the terms: -5y + -4y2 + (-2 + 2y + 2y2) = 0 Remove parenthesis around (-2 + 2y + 2y2) -5y + -4y2 + -2 + 2y + 2y2 = 0 Reorder the terms: -2 + -5y + 2y + -4y2 + 2y2 = 0 Combine like terms: -5y + 2y = -3y -2 + -3y + -4y2 + 2y2 = 0 Combine like terms: -4y2 + 2y2 = -2y2 -2 + -3y + -2y2 = 0 Solving -2 + -3y + -2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 3y + 2y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 3y + 2y2)' equal to zero and attempt to solve: Simplifying 2 + 3y + 2y2 = 0 Solving 2 + 3y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 1.5y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.5y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + 1.5y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.5y + y2 = 0 + -1 1.5y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 1.5y + y2 = -1 The y term is 1.5y. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5y + 0.5625 + y2 = -1 + 0.5625 Reorder the terms: 0.5625 + 1.5y + y2 = -1 + 0.5625 Combine like terms: -1 + 0.5625 = -0.4375 0.5625 + 1.5y + y2 = -0.4375 Factor a perfect square on the left side: (y + 0.75)(y + 0.75) = -0.4375 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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