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Simplifying 27y2 + 36y + 27 = 0 Reorder the terms: 27 + 36y + 27y2 = 0 Solving 27 + 36y + 27y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '9'. 9(3 + 4y + 3y2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(3 + 4y + 3y2)' equal to zero and attempt to solve: Simplifying 3 + 4y + 3y2 = 0 Solving 3 + 4y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1 + 1.333333333y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.333333333y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + 1.333333333y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.333333333y + y2 = 0 + -1 1.333333333y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 1.333333333y + y2 = -1 The y term is 1.333333333y. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333y + 0.4444444442 + y2 = -1 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333y + y2 = -1 + 0.4444444442 Combine like terms: -1 + 0.4444444442 = -0.5555555558 0.4444444442 + 1.333333333y + y2 = -0.5555555558 Factor a perfect square on the left side: (y + 0.6666666665)(y + 0.6666666665) = -0.5555555558 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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