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Simplifying 5y2 + 45y + 105 = 0 Reorder the terms: 105 + 45y + 5y2 = 0 Solving 105 + 45y + 5y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5'. 5(21 + 9y + y2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(21 + 9y + y2)' equal to zero and attempt to solve: Simplifying 21 + 9y + y2 = 0 Solving 21 + 9y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 9y + -21 + y2 = 0 + -21 Reorder the terms: 21 + -21 + 9y + y2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 9y + y2 = 0 + -21 9y + y2 = 0 + -21 Combine like terms: 0 + -21 = -21 9y + y2 = -21 The y term is 9y. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9y + 20.25 + y2 = -21 + 20.25 Reorder the terms: 20.25 + 9y + y2 = -21 + 20.25 Combine like terms: -21 + 20.25 = -0.75 20.25 + 9y + y2 = -0.75 Factor a perfect square on the left side: (y + 4.5)(y + 4.5) = -0.75 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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