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Simplifying 2y2 + -37y + 48 = 0 Reorder the terms: 48 + -37y + 2y2 = 0 Solving 48 + -37y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 24 + -18.5y + y2 = 0 Move the constant term to the right: Add '-24' to each side of the equation. 24 + -18.5y + -24 + y2 = 0 + -24 Reorder the terms: 24 + -24 + -18.5y + y2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -18.5y + y2 = 0 + -24 -18.5y + y2 = 0 + -24 Combine like terms: 0 + -24 = -24 -18.5y + y2 = -24 The y term is -18.5y. Take half its coefficient (-9.25). Square it (85.5625) and add it to both sides. Add '85.5625' to each side of the equation. -18.5y + 85.5625 + y2 = -24 + 85.5625 Reorder the terms: 85.5625 + -18.5y + y2 = -24 + 85.5625 Combine like terms: -24 + 85.5625 = 61.5625 85.5625 + -18.5y + y2 = 61.5625 Factor a perfect square on the left side: (y + -9.25)(y + -9.25) = 61.5625 Calculate the square root of the right side: 7.846177413 Break this problem into two subproblems by setting (y + -9.25) equal to 7.846177413 and -7.846177413.Subproblem 1
y + -9.25 = 7.846177413 Simplifying y + -9.25 = 7.846177413 Reorder the terms: -9.25 + y = 7.846177413 Solving -9.25 + y = 7.846177413 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.25' to each side of the equation. -9.25 + 9.25 + y = 7.846177413 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + y = 7.846177413 + 9.25 y = 7.846177413 + 9.25 Combine like terms: 7.846177413 + 9.25 = 17.096177413 y = 17.096177413 Simplifying y = 17.096177413Subproblem 2
y + -9.25 = -7.846177413 Simplifying y + -9.25 = -7.846177413 Reorder the terms: -9.25 + y = -7.846177413 Solving -9.25 + y = -7.846177413 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9.25' to each side of the equation. -9.25 + 9.25 + y = -7.846177413 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + y = -7.846177413 + 9.25 y = -7.846177413 + 9.25 Combine like terms: -7.846177413 + 9.25 = 1.403822587 y = 1.403822587 Simplifying y = 1.403822587Solution
The solution to the problem is based on the solutions from the subproblems. y = {17.096177413, 1.403822587}
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