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Simplifying (6y + 6)(2y + -3) = -2y(5y + 4) + -28 Reorder the terms: (6 + 6y)(2y + -3) = -2y(5y + 4) + -28 Reorder the terms: (6 + 6y)(-3 + 2y) = -2y(5y + 4) + -28 Multiply (6 + 6y) * (-3 + 2y) (6(-3 + 2y) + 6y * (-3 + 2y)) = -2y(5y + 4) + -28 ((-3 * 6 + 2y * 6) + 6y * (-3 + 2y)) = -2y(5y + 4) + -28 ((-18 + 12y) + 6y * (-3 + 2y)) = -2y(5y + 4) + -28 (-18 + 12y + (-3 * 6y + 2y * 6y)) = -2y(5y + 4) + -28 (-18 + 12y + (-18y + 12y2)) = -2y(5y + 4) + -28 Combine like terms: 12y + -18y = -6y (-18 + -6y + 12y2) = -2y(5y + 4) + -28 Reorder the terms: -18 + -6y + 12y2 = -2y(4 + 5y) + -28 -18 + -6y + 12y2 = (4 * -2y + 5y * -2y) + -28 -18 + -6y + 12y2 = (-8y + -10y2) + -28 Reorder the terms: -18 + -6y + 12y2 = -28 + -8y + -10y2 Solving -18 + -6y + 12y2 = -28 + -8y + -10y2 Solving for variable 'y'. Reorder the terms: -18 + 28 + -6y + 8y + 12y2 + 10y2 = -28 + -8y + -10y2 + 28 + 8y + 10y2 Combine like terms: -18 + 28 = 10 10 + -6y + 8y + 12y2 + 10y2 = -28 + -8y + -10y2 + 28 + 8y + 10y2 Combine like terms: -6y + 8y = 2y 10 + 2y + 12y2 + 10y2 = -28 + -8y + -10y2 + 28 + 8y + 10y2 Combine like terms: 12y2 + 10y2 = 22y2 10 + 2y + 22y2 = -28 + -8y + -10y2 + 28 + 8y + 10y2 Reorder the terms: 10 + 2y + 22y2 = -28 + 28 + -8y + 8y + -10y2 + 10y2 Combine like terms: -28 + 28 = 0 10 + 2y + 22y2 = 0 + -8y + 8y + -10y2 + 10y2 10 + 2y + 22y2 = -8y + 8y + -10y2 + 10y2 Combine like terms: -8y + 8y = 0 10 + 2y + 22y2 = 0 + -10y2 + 10y2 10 + 2y + 22y2 = -10y2 + 10y2 Combine like terms: -10y2 + 10y2 = 0 10 + 2y + 22y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + y + 11y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + y + 11y2)' equal to zero and attempt to solve: Simplifying 5 + y + 11y2 = 0 Solving 5 + y + 11y2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.4545454545 + 0.09090909091y + y2 = 0 Move the constant term to the right: Add '-0.4545454545' to each side of the equation. 0.4545454545 + 0.09090909091y + -0.4545454545 + y2 = 0 + -0.4545454545 Reorder the terms: 0.4545454545 + -0.4545454545 + 0.09090909091y + y2 = 0 + -0.4545454545 Combine like terms: 0.4545454545 + -0.4545454545 = 0.0000000000 0.0000000000 + 0.09090909091y + y2 = 0 + -0.4545454545 0.09090909091y + y2 = 0 + -0.4545454545 Combine like terms: 0 + -0.4545454545 = -0.4545454545 0.09090909091y + y2 = -0.4545454545 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. 0.09090909091y + 0.25 + y2 = -0.4545454545 + 0.25 Reorder the terms: 0.25 + 0.09090909091y + y2 = -0.4545454545 + 0.25 Combine like terms: -0.4545454545 + 0.25 = -0.2045454545 0.25 + 0.09090909091y + y2 = -0.2045454545 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -0.2045454545 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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