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Simplifying (Y + -7) = 2Y2 + -19Y + 55 Reorder the terms: (-7 + Y) = 2Y2 + -19Y + 55 Remove parenthesis around (-7 + Y) -7 + Y = 2Y2 + -19Y + 55 Reorder the terms: -7 + Y = 55 + -19Y + 2Y2 Solving -7 + Y = 55 + -19Y + 2Y2 Solving for variable 'Y'. Reorder the terms: -7 + -55 + Y + 19Y + -2Y2 = 55 + -19Y + 2Y2 + -55 + 19Y + -2Y2 Combine like terms: -7 + -55 = -62 -62 + Y + 19Y + -2Y2 = 55 + -19Y + 2Y2 + -55 + 19Y + -2Y2 Combine like terms: Y + 19Y = 20Y -62 + 20Y + -2Y2 = 55 + -19Y + 2Y2 + -55 + 19Y + -2Y2 Reorder the terms: -62 + 20Y + -2Y2 = 55 + -55 + -19Y + 19Y + 2Y2 + -2Y2 Combine like terms: 55 + -55 = 0 -62 + 20Y + -2Y2 = 0 + -19Y + 19Y + 2Y2 + -2Y2 -62 + 20Y + -2Y2 = -19Y + 19Y + 2Y2 + -2Y2 Combine like terms: -19Y + 19Y = 0 -62 + 20Y + -2Y2 = 0 + 2Y2 + -2Y2 -62 + 20Y + -2Y2 = 2Y2 + -2Y2 Combine like terms: 2Y2 + -2Y2 = 0 -62 + 20Y + -2Y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-31 + 10Y + -1Y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-31 + 10Y + -1Y2)' equal to zero and attempt to solve: Simplifying -31 + 10Y + -1Y2 = 0 Solving -31 + 10Y + -1Y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 31 + -10Y + Y2 = 0 Move the constant term to the right: Add '-31' to each side of the equation. 31 + -10Y + -31 + Y2 = 0 + -31 Reorder the terms: 31 + -31 + -10Y + Y2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -10Y + Y2 = 0 + -31 -10Y + Y2 = 0 + -31 Combine like terms: 0 + -31 = -31 -10Y + Y2 = -31 The Y term is -10Y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10Y + 25 + Y2 = -31 + 25 Reorder the terms: 25 + -10Y + Y2 = -31 + 25 Combine like terms: -31 + 25 = -6 25 + -10Y + Y2 = -6 Factor a perfect square on the left side: (Y + -5)(Y + -5) = -6 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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