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Simplifying (-6y2 + -6y) + (3y2 + y + -5) = 0 Reorder the terms: (-6y + -6y2) + (3y2 + y + -5) = 0 Remove parenthesis around (-6y + -6y2) -6y + -6y2 + (3y2 + y + -5) = 0 Reorder the terms: -6y + -6y2 + (-5 + y + 3y2) = 0 Remove parenthesis around (-5 + y + 3y2) -6y + -6y2 + -5 + y + 3y2 = 0 Reorder the terms: -5 + -6y + y + -6y2 + 3y2 = 0 Combine like terms: -6y + y = -5y -5 + -5y + -6y2 + 3y2 = 0 Combine like terms: -6y2 + 3y2 = -3y2 -5 + -5y + -3y2 = 0 Solving -5 + -5y + -3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 5y + 3y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 5y + 3y2)' equal to zero and attempt to solve: Simplifying 5 + 5y + 3y2 = 0 Solving 5 + 5y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 1.666666667y + y2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 1.666666667y + -1.666666667 + y2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 1.666666667y + y2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 1.666666667y + y2 = 0 + -1.666666667 1.666666667y + y2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 1.666666667y + y2 = -1.666666667 The y term is 1.666666667y. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667y + 0.6944444447 + y2 = -1.666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667y + y2 = -1.666666667 + 0.6944444447 Combine like terms: -1.666666667 + 0.6944444447 = -0.9722222223 0.6944444447 + 1.666666667y + y2 = -0.9722222223 Factor a perfect square on the left side: (y + 0.8333333335)(y + 0.8333333335) = -0.9722222223 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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