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Simplifying 6y2 + 2y = -48 Reorder the terms: 2y + 6y2 = -48 Solving 2y + 6y2 = -48 Solving for variable 'y'. Reorder the terms: 48 + 2y + 6y2 = -48 + 48 Combine like terms: -48 + 48 = 0 48 + 2y + 6y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(24 + y + 3y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + y + 3y2)' equal to zero and attempt to solve: Simplifying 24 + y + 3y2 = 0 Solving 24 + y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 8 + 0.3333333333y + y2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + 0.3333333333y + -8 + y2 = 0 + -8 Reorder the terms: 8 + -8 + 0.3333333333y + y2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 0.3333333333y + y2 = 0 + -8 0.3333333333y + y2 = 0 + -8 Combine like terms: 0 + -8 = -8 0.3333333333y + y2 = -8 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. 0.3333333333y + 0.25 + y2 = -8 + 0.25 Reorder the terms: 0.25 + 0.3333333333y + y2 = -8 + 0.25 Combine like terms: -8 + 0.25 = -7.75 0.25 + 0.3333333333y + y2 = -7.75 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -7.75 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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