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Simplifying 17 = 2y2 + 36y + 324 Reorder the terms: 17 = 324 + 36y + 2y2 Solving 17 = 324 + 36y + 2y2 Solving for variable 'y'. Combine like terms: 17 + -324 = -307 -307 + -36y + -2y2 = 324 + 36y + 2y2 + -324 + -36y + -2y2 Reorder the terms: -307 + -36y + -2y2 = 324 + -324 + 36y + -36y + 2y2 + -2y2 Combine like terms: 324 + -324 = 0 -307 + -36y + -2y2 = 0 + 36y + -36y + 2y2 + -2y2 -307 + -36y + -2y2 = 36y + -36y + 2y2 + -2y2 Combine like terms: 36y + -36y = 0 -307 + -36y + -2y2 = 0 + 2y2 + -2y2 -307 + -36y + -2y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 -307 + -36y + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(307 + 36y + 2y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(307 + 36y + 2y2)' equal to zero and attempt to solve: Simplifying 307 + 36y + 2y2 = 0 Solving 307 + 36y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 153.5 + 18y + y2 = 0 Move the constant term to the right: Add '-153.5' to each side of the equation. 153.5 + 18y + -153.5 + y2 = 0 + -153.5 Reorder the terms: 153.5 + -153.5 + 18y + y2 = 0 + -153.5 Combine like terms: 153.5 + -153.5 = 0.0 0.0 + 18y + y2 = 0 + -153.5 18y + y2 = 0 + -153.5 Combine like terms: 0 + -153.5 = -153.5 18y + y2 = -153.5 The y term is 18y. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18y + 81 + y2 = -153.5 + 81 Reorder the terms: 81 + 18y + y2 = -153.5 + 81 Combine like terms: -153.5 + 81 = -72.5 81 + 18y + y2 = -72.5 Factor a perfect square on the left side: (y + 9)(y + 9) = -72.5 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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