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Simplifying y = 2y2 + 6y + 40 Reorder the terms: y = 40 + 6y + 2y2 Solving y = 40 + 6y + 2y2 Solving for variable 'y'. Reorder the terms: -40 + y + -6y + -2y2 = 40 + 6y + 2y2 + -40 + -6y + -2y2 Combine like terms: y + -6y = -5y -40 + -5y + -2y2 = 40 + 6y + 2y2 + -40 + -6y + -2y2 Reorder the terms: -40 + -5y + -2y2 = 40 + -40 + 6y + -6y + 2y2 + -2y2 Combine like terms: 40 + -40 = 0 -40 + -5y + -2y2 = 0 + 6y + -6y + 2y2 + -2y2 -40 + -5y + -2y2 = 6y + -6y + 2y2 + -2y2 Combine like terms: 6y + -6y = 0 -40 + -5y + -2y2 = 0 + 2y2 + -2y2 -40 + -5y + -2y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 -40 + -5y + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(40 + 5y + 2y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(40 + 5y + 2y2)' equal to zero and attempt to solve: Simplifying 40 + 5y + 2y2 = 0 Solving 40 + 5y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 20 + 2.5y + y2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + 2.5y + -20 + y2 = 0 + -20 Reorder the terms: 20 + -20 + 2.5y + y2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 2.5y + y2 = 0 + -20 2.5y + y2 = 0 + -20 Combine like terms: 0 + -20 = -20 2.5y + y2 = -20 The y term is 2.5y. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5y + 1.5625 + y2 = -20 + 1.5625 Reorder the terms: 1.5625 + 2.5y + y2 = -20 + 1.5625 Combine like terms: -20 + 1.5625 = -18.4375 1.5625 + 2.5y + y2 = -18.4375 Factor a perfect square on the left side: (y + 1.25)(y + 1.25) = -18.4375 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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