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Simplifying 2y2 + -20y + 25 = 12 Reorder the terms: 25 + -20y + 2y2 = 12 Solving 25 + -20y + 2y2 = 12 Solving for variable 'y'. Reorder the terms: 25 + -12 + -20y + 2y2 = 12 + -12 Combine like terms: 25 + -12 = 13 13 + -20y + 2y2 = 12 + -12 Combine like terms: 12 + -12 = 0 13 + -20y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + -10y + y2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -10y + -6.5 + y2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -10y + y2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -10y + y2 = 0 + -6.5 -10y + y2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -10y + y2 = -6.5 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = -6.5 + 25 Reorder the terms: 25 + -10y + y2 = -6.5 + 25 Combine like terms: -6.5 + 25 = 18.5 25 + -10y + y2 = 18.5 Factor a perfect square on the left side: (y + -5)(y + -5) = 18.5 Calculate the square root of the right side: 4.301162634 Break this problem into two subproblems by setting (y + -5) equal to 4.301162634 and -4.301162634.Subproblem 1
y + -5 = 4.301162634 Simplifying y + -5 = 4.301162634 Reorder the terms: -5 + y = 4.301162634 Solving -5 + y = 4.301162634 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 4.301162634 + 5 Combine like terms: -5 + 5 = 0 0 + y = 4.301162634 + 5 y = 4.301162634 + 5 Combine like terms: 4.301162634 + 5 = 9.301162634 y = 9.301162634 Simplifying y = 9.301162634Subproblem 2
y + -5 = -4.301162634 Simplifying y + -5 = -4.301162634 Reorder the terms: -5 + y = -4.301162634 Solving -5 + y = -4.301162634 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -4.301162634 + 5 Combine like terms: -5 + 5 = 0 0 + y = -4.301162634 + 5 y = -4.301162634 + 5 Combine like terms: -4.301162634 + 5 = 0.698837366 y = 0.698837366 Simplifying y = 0.698837366Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.301162634, 0.698837366}
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