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Simplifying 2y2 + 28y + 102 = 0 Reorder the terms: 102 + 28y + 2y2 = 0 Solving 102 + 28y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(51 + 14y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(51 + 14y + y2)' equal to zero and attempt to solve: Simplifying 51 + 14y + y2 = 0 Solving 51 + 14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-51' to each side of the equation. 51 + 14y + -51 + y2 = 0 + -51 Reorder the terms: 51 + -51 + 14y + y2 = 0 + -51 Combine like terms: 51 + -51 = 0 0 + 14y + y2 = 0 + -51 14y + y2 = 0 + -51 Combine like terms: 0 + -51 = -51 14y + y2 = -51 The y term is 14y. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14y + 49 + y2 = -51 + 49 Reorder the terms: 49 + 14y + y2 = -51 + 49 Combine like terms: -51 + 49 = -2 49 + 14y + y2 = -2 Factor a perfect square on the left side: (y + 7)(y + 7) = -2 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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