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Simplifying 315y + 3y2 = 10 Solving 315y + 3y2 = 10 Solving for variable 'y'. Reorder the terms: -10 + 315y + 3y2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 315y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + 105y + y2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + 105y + 3.333333333 + y2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + 105y + y2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + 105y + y2 = 0 + 3.333333333 105y + y2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 105y + y2 = 3.333333333 The y term is 105y. Take half its coefficient (52.5). Square it (2756.25) and add it to both sides. Add '2756.25' to each side of the equation. 105y + 2756.25 + y2 = 3.333333333 + 2756.25 Reorder the terms: 2756.25 + 105y + y2 = 3.333333333 + 2756.25 Combine like terms: 3.333333333 + 2756.25 = 2759.583333333 2756.25 + 105y + y2 = 2759.583333333 Factor a perfect square on the left side: (y + 52.5)(y + 52.5) = 2759.583333333 Calculate the square root of the right side: 52.531736439 Break this problem into two subproblems by setting (y + 52.5) equal to 52.531736439 and -52.531736439.Subproblem 1
y + 52.5 = 52.531736439 Simplifying y + 52.5 = 52.531736439 Reorder the terms: 52.5 + y = 52.531736439 Solving 52.5 + y = 52.531736439 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + y = 52.531736439 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + y = 52.531736439 + -52.5 y = 52.531736439 + -52.5 Combine like terms: 52.531736439 + -52.5 = 0.031736439 y = 0.031736439 Simplifying y = 0.031736439Subproblem 2
y + 52.5 = -52.531736439 Simplifying y + 52.5 = -52.531736439 Reorder the terms: 52.5 + y = -52.531736439 Solving 52.5 + y = -52.531736439 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-52.5' to each side of the equation. 52.5 + -52.5 + y = -52.531736439 + -52.5 Combine like terms: 52.5 + -52.5 = 0.0 0.0 + y = -52.531736439 + -52.5 y = -52.531736439 + -52.5 Combine like terms: -52.531736439 + -52.5 = -105.031736439 y = -105.031736439 Simplifying y = -105.031736439Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.031736439, -105.031736439}
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