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Simplifying -8y2 + 28y = 60 Reorder the terms: 28y + -8y2 = 60 Solving 28y + -8y2 = 60 Solving for variable 'y'. Reorder the terms: -60 + 28y + -8y2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + 28y + -8y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + 7y + -2y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + 7y + -2y2)' equal to zero and attempt to solve: Simplifying -15 + 7y + -2y2 = 0 Solving -15 + 7y + -2y2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 7.5 + -3.5y + y2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -3.5y + -7.5 + y2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -3.5y + y2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -3.5y + y2 = 0 + -7.5 -3.5y + y2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -3.5y + y2 = -7.5 The y term is -3.5y. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5y + 3.0625 + y2 = -7.5 + 3.0625 Reorder the terms: 3.0625 + -3.5y + y2 = -7.5 + 3.0625 Combine like terms: -7.5 + 3.0625 = -4.4375 3.0625 + -3.5y + y2 = -4.4375 Factor a perfect square on the left side: (y + -1.75)(y + -1.75) = -4.4375 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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