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Simplifying y2 + 10y + 25 = 85 Reorder the terms: 25 + 10y + y2 = 85 Solving 25 + 10y + y2 = 85 Solving for variable 'y'. Reorder the terms: 25 + -85 + 10y + y2 = 85 + -85 Combine like terms: 25 + -85 = -60 -60 + 10y + y2 = 85 + -85 Combine like terms: 85 + -85 = 0 -60 + 10y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 10y + 60 + y2 = 0 + 60 Reorder the terms: -60 + 60 + 10y + y2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 10y + y2 = 0 + 60 10y + y2 = 0 + 60 Combine like terms: 0 + 60 = 60 10y + y2 = 60 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 = 60 + 25 Reorder the terms: 25 + 10y + y2 = 60 + 25 Combine like terms: 60 + 25 = 85 25 + 10y + y2 = 85 Factor a perfect square on the left side: (y + 5)(y + 5) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (y + 5) equal to 9.219544457 and -9.219544457.Subproblem 1
y + 5 = 9.219544457 Simplifying y + 5 = 9.219544457 Reorder the terms: 5 + y = 9.219544457 Solving 5 + y = 9.219544457 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 = 9.219544457 + -5 Combine like terms: 5 + -5 = 0 0 + y = 9.219544457 + -5 y = 9.219544457 + -5 Combine like terms: 9.219544457 + -5 = 4.219544457 y = 4.219544457 Simplifying y = 4.219544457Subproblem 2
y + 5 = -9.219544457 Simplifying y + 5 = -9.219544457 Reorder the terms: 5 + y = -9.219544457 Solving 5 + y = -9.219544457 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 = -9.219544457 + -5 Combine like terms: 5 + -5 = 0 0 + y = -9.219544457 + -5 y = -9.219544457 + -5 Combine like terms: -9.219544457 + -5 = -14.219544457 y = -14.219544457 Simplifying y = -14.219544457Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.219544457, -14.219544457}
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