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Simplifying 15y + -540 + 15y = 2y2 + -72 Reorder the terms: -540 + 15y + 15y = 2y2 + -72 Combine like terms: 15y + 15y = 30y -540 + 30y = 2y2 + -72 Reorder the terms: -540 + 30y = -72 + 2y2 Solving -540 + 30y = -72 + 2y2 Solving for variable 'y'. Reorder the terms: -540 + 72 + 30y + -2y2 = -72 + 2y2 + 72 + -2y2 Combine like terms: -540 + 72 = -468 -468 + 30y + -2y2 = -72 + 2y2 + 72 + -2y2 Reorder the terms: -468 + 30y + -2y2 = -72 + 72 + 2y2 + -2y2 Combine like terms: -72 + 72 = 0 -468 + 30y + -2y2 = 0 + 2y2 + -2y2 -468 + 30y + -2y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 -468 + 30y + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-234 + 15y + -1y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-234 + 15y + -1y2)' equal to zero and attempt to solve: Simplifying -234 + 15y + -1y2 = 0 Solving -234 + 15y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 234 + -15y + y2 = 0 Move the constant term to the right: Add '-234' to each side of the equation. 234 + -15y + -234 + y2 = 0 + -234 Reorder the terms: 234 + -234 + -15y + y2 = 0 + -234 Combine like terms: 234 + -234 = 0 0 + -15y + y2 = 0 + -234 -15y + y2 = 0 + -234 Combine like terms: 0 + -234 = -234 -15y + y2 = -234 The y term is -15y. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15y + 56.25 + y2 = -234 + 56.25 Reorder the terms: 56.25 + -15y + y2 = -234 + 56.25 Combine like terms: -234 + 56.25 = -177.75 56.25 + -15y + y2 = -177.75 Factor a perfect square on the left side: (y + -7.5)(y + -7.5) = -177.75 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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