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Simplifying 6y2 + 32y + 72 = 0 Reorder the terms: 72 + 32y + 6y2 = 0 Solving 72 + 32y + 6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(36 + 16y + 3y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(36 + 16y + 3y2)' equal to zero and attempt to solve: Simplifying 36 + 16y + 3y2 = 0 Solving 36 + 16y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 12 + 5.333333333y + y2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + 5.333333333y + -12 + y2 = 0 + -12 Reorder the terms: 12 + -12 + 5.333333333y + y2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 5.333333333y + y2 = 0 + -12 5.333333333y + y2 = 0 + -12 Combine like terms: 0 + -12 = -12 5.333333333y + y2 = -12 The y term is 5.333333333y. Take half its coefficient (2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. 5.333333333y + 7.111111113 + y2 = -12 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333y + y2 = -12 + 7.111111113 Combine like terms: -12 + 7.111111113 = -4.888888887 7.111111113 + 5.333333333y + y2 = -4.888888887 Factor a perfect square on the left side: (y + 2.666666667)(y + 2.666666667) = -4.888888887 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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