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Simplifying 25y2 + -80y + 6 = 0 Reorder the terms: 6 + -80y + 25y2 = 0 Solving 6 + -80y + 25y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.24 + -3.2y + y2 = 0 Move the constant term to the right: Add '-0.24' to each side of the equation. 0.24 + -3.2y + -0.24 + y2 = 0 + -0.24 Reorder the terms: 0.24 + -0.24 + -3.2y + y2 = 0 + -0.24 Combine like terms: 0.24 + -0.24 = 0.00 0.00 + -3.2y + y2 = 0 + -0.24 -3.2y + y2 = 0 + -0.24 Combine like terms: 0 + -0.24 = -0.24 -3.2y + y2 = -0.24 The y term is -3.2y. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2y + 2.56 + y2 = -0.24 + 2.56 Reorder the terms: 2.56 + -3.2y + y2 = -0.24 + 2.56 Combine like terms: -0.24 + 2.56 = 2.32 2.56 + -3.2y + y2 = 2.32 Factor a perfect square on the left side: (y + -1.6)(y + -1.6) = 2.32 Calculate the square root of the right side: 1.523154621 Break this problem into two subproblems by setting (y + -1.6) equal to 1.523154621 and -1.523154621.Subproblem 1
y + -1.6 = 1.523154621 Simplifying y + -1.6 = 1.523154621 Reorder the terms: -1.6 + y = 1.523154621 Solving -1.6 + y = 1.523154621 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + y = 1.523154621 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + y = 1.523154621 + 1.6 y = 1.523154621 + 1.6 Combine like terms: 1.523154621 + 1.6 = 3.123154621 y = 3.123154621 Simplifying y = 3.123154621Subproblem 2
y + -1.6 = -1.523154621 Simplifying y + -1.6 = -1.523154621 Reorder the terms: -1.6 + y = -1.523154621 Solving -1.6 + y = -1.523154621 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + y = -1.523154621 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + y = -1.523154621 + 1.6 y = -1.523154621 + 1.6 Combine like terms: -1.523154621 + 1.6 = 0.076845379 y = 0.076845379 Simplifying y = 0.076845379Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.123154621, 0.076845379}
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