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Simplifying (3 + -2y)(3 + -2y) + -4y + -4y = -33 Multiply (3 + -2y) * (3 + -2y) (3(3 + -2y) + -2y * (3 + -2y)) + -4y + -4y = -33 ((3 * 3 + -2y * 3) + -2y * (3 + -2y)) + -4y + -4y = -33 ((9 + -6y) + -2y * (3 + -2y)) + -4y + -4y = -33 (9 + -6y + (3 * -2y + -2y * -2y)) + -4y + -4y = -33 (9 + -6y + (-6y + 4y2)) + -4y + -4y = -33 Combine like terms: -6y + -6y = -12y (9 + -12y + 4y2) + -4y + -4y = -33 Reorder the terms: 9 + -12y + -4y + -4y + 4y2 = -33 Combine like terms: -12y + -4y = -16y 9 + -16y + -4y + 4y2 = -33 Combine like terms: -16y + -4y = -20y 9 + -20y + 4y2 = -33 Solving 9 + -20y + 4y2 = -33 Solving for variable 'y'. Reorder the terms: 9 + 33 + -20y + 4y2 = -33 + 33 Combine like terms: 9 + 33 = 42 42 + -20y + 4y2 = -33 + 33 Combine like terms: -33 + 33 = 0 42 + -20y + 4y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(21 + -10y + 2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + -10y + 2y2)' equal to zero and attempt to solve: Simplifying 21 + -10y + 2y2 = 0 Solving 21 + -10y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.5 + -5y + y2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + -5y + -10.5 + y2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + -5y + y2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + -5y + y2 = 0 + -10.5 -5y + y2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 -5y + y2 = -10.5 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = -10.5 + 6.25 Reorder the terms: 6.25 + -5y + y2 = -10.5 + 6.25 Combine like terms: -10.5 + 6.25 = -4.25 6.25 + -5y + y2 = -4.25 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = -4.25 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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