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Simplifying 3y7 + 9y6 + 39y5 = 0 Reorder the terms: 39y5 + 9y6 + 3y7 = 0 Solving 39y5 + 9y6 + 3y7 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3y5'. 3y5(13 + 3y + y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'y5' equal to zero and attempt to solve: Simplifying y5 = 0 Solving y5 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y5 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(13 + 3y + y2)' equal to zero and attempt to solve: Simplifying 13 + 3y + y2 = 0 Solving 13 + 3y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-13' to each side of the equation. 13 + 3y + -13 + y2 = 0 + -13 Reorder the terms: 13 + -13 + 3y + y2 = 0 + -13 Combine like terms: 13 + -13 = 0 0 + 3y + y2 = 0 + -13 3y + y2 = 0 + -13 Combine like terms: 0 + -13 = -13 3y + y2 = -13 The y term is 3y. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y + 2.25 + y2 = -13 + 2.25 Reorder the terms: 2.25 + 3y + y2 = -13 + 2.25 Combine like terms: -13 + 2.25 = -10.75 2.25 + 3y + y2 = -10.75 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = -10.75 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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