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Simplifying 12 + -2(3y + -2)(3y + 2) + -1(2y + 5)(2y + 5) = 0 Reorder the terms: 12 + -2(-2 + 3y)(3y + 2) + -1(2y + 5)(2y + 5) = 0 Reorder the terms: 12 + -2(-2 + 3y)(2 + 3y) + -1(2y + 5)(2y + 5) = 0 Multiply (-2 + 3y) * (2 + 3y) 12 + -2(-2(2 + 3y) + 3y * (2 + 3y)) + -1(2y + 5)(2y + 5) = 0 12 + -2((2 * -2 + 3y * -2) + 3y * (2 + 3y)) + -1(2y + 5)(2y + 5) = 0 12 + -2((-4 + -6y) + 3y * (2 + 3y)) + -1(2y + 5)(2y + 5) = 0 12 + -2(-4 + -6y + (2 * 3y + 3y * 3y)) + -1(2y + 5)(2y + 5) = 0 12 + -2(-4 + -6y + (6y + 9y2)) + -1(2y + 5)(2y + 5) = 0 Combine like terms: -6y + 6y = 0 12 + -2(-4 + 0 + 9y2) + -1(2y + 5)(2y + 5) = 0 12 + -2(-4 + 9y2) + -1(2y + 5)(2y + 5) = 0 12 + (-4 * -2 + 9y2 * -2) + -1(2y + 5)(2y + 5) = 0 12 + (8 + -18y2) + -1(2y + 5)(2y + 5) = 0 Reorder the terms: 12 + 8 + -18y2 + -1(5 + 2y)(2y + 5) = 0 Reorder the terms: 12 + 8 + -18y2 + -1(5 + 2y)(5 + 2y) = 0 Multiply (5 + 2y) * (5 + 2y) 12 + 8 + -18y2 + -1(5(5 + 2y) + 2y * (5 + 2y)) = 0 12 + 8 + -18y2 + -1((5 * 5 + 2y * 5) + 2y * (5 + 2y)) = 0 12 + 8 + -18y2 + -1((25 + 10y) + 2y * (5 + 2y)) = 0 12 + 8 + -18y2 + -1(25 + 10y + (5 * 2y + 2y * 2y)) = 0 12 + 8 + -18y2 + -1(25 + 10y + (10y + 4y2)) = 0 Combine like terms: 10y + 10y = 20y 12 + 8 + -18y2 + -1(25 + 20y + 4y2) = 0 12 + 8 + -18y2 + (25 * -1 + 20y * -1 + 4y2 * -1) = 0 12 + 8 + -18y2 + (-25 + -20y + -4y2) = 0 Reorder the terms: 12 + 8 + -25 + -20y + -18y2 + -4y2 = 0 Combine like terms: 12 + 8 = 20 20 + -25 + -20y + -18y2 + -4y2 = 0 Combine like terms: 20 + -25 = -5 -5 + -20y + -18y2 + -4y2 = 0 Combine like terms: -18y2 + -4y2 = -22y2 -5 + -20y + -22y2 = 0 Solving -5 + -20y + -22y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 20y + 22y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 20y + 22y2)' equal to zero and attempt to solve: Simplifying 5 + 20y + 22y2 = 0 Solving 5 + 20y + 22y2 = 0 Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. 0.2272727273 + 0.9090909091y + y2 = 0 Move the constant term to the right: Add '-0.2272727273' to each side of the equation. 0.2272727273 + 0.9090909091y + -0.2272727273 + y2 = 0 + -0.2272727273 Reorder the terms: 0.2272727273 + -0.2272727273 + 0.9090909091y + y2 = 0 + -0.2272727273 Combine like terms: 0.2272727273 + -0.2272727273 = 0.0000000000 0.0000000000 + 0.9090909091y + y2 = 0 + -0.2272727273 0.9090909091y + y2 = 0 + -0.2272727273 Combine like terms: 0 + -0.2272727273 = -0.2272727273 0.9090909091y + y2 = -0.2272727273 The y term is 0.9090909091y. Take half its coefficient (0.4545454546). Square it (0.2066115703) and add it to both sides. Add '0.2066115703' to each side of the equation. 0.9090909091y + 0.2066115703 + y2 = -0.2272727273 + 0.2066115703 Reorder the terms: 0.2066115703 + 0.9090909091y + y2 = -0.2272727273 + 0.2066115703 Combine like terms: -0.2272727273 + 0.2066115703 = -0.020661157 0.2066115703 + 0.9090909091y + y2 = -0.020661157 Factor a perfect square on the left side: (y + 0.4545454546)(y + 0.4545454546) = -0.020661157 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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