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Simplifying -4 + 3y + 5y2 + 8 + 3y + y2 = 0 Reorder the terms: -4 + 8 + 3y + 3y + 5y2 + y2 = 0 Combine like terms: -4 + 8 = 4 4 + 3y + 3y + 5y2 + y2 = 0 Combine like terms: 3y + 3y = 6y 4 + 6y + 5y2 + y2 = 0 Combine like terms: 5y2 + y2 = 6y2 4 + 6y + 6y2 = 0 Solving 4 + 6y + 6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(2 + 3y + 3y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + 3y + 3y2)' equal to zero and attempt to solve: Simplifying 2 + 3y + 3y2 = 0 Solving 2 + 3y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + y + y2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + y + -0.6666666667 + y2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + y + y2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + y + y2 = 0 + -0.6666666667 y + y2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 y + y2 = -0.6666666667 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. + 0.25 + y2 = -0.6666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + y2 = -0.6666666667 + 0.25 Combine like terms: -0.6666666667 + 0.25 = -0.4166666667 1.25 + y2 = -0.4166666667 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -0.4166666667 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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