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Simplifying 2y2 + -20y + 25 = 0 Reorder the terms: 25 + -20y + 2y2 = 0 Solving 25 + -20y + 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'. 12.5 + -10y + y2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -10y + -12.5 + y2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -10y + y2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -10y + y2 = 0 + -12.5 -10y + y2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -10y + y2 = -12.5 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 = -12.5 + 25 Reorder the terms: 25 + -10y + y2 = -12.5 + 25 Combine like terms: -12.5 + 25 = 12.5 25 + -10y + y2 = 12.5 Factor a perfect square on the left side: (y + -5)(y + -5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (y + -5) equal to 3.535533906 and -3.535533906.Subproblem 1
y + -5 = 3.535533906 Simplifying y + -5 = 3.535533906 Reorder the terms: -5 + y = 3.535533906 Solving -5 + y = 3.535533906 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 = 3.535533906 + 5 Combine like terms: -5 + 5 = 0 0 + y = 3.535533906 + 5 y = 3.535533906 + 5 Combine like terms: 3.535533906 + 5 = 8.535533906 y = 8.535533906 Simplifying y = 8.535533906Subproblem 2
y + -5 = -3.535533906 Simplifying y + -5 = -3.535533906 Reorder the terms: -5 + y = -3.535533906 Solving -5 + y = -3.535533906 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 = -3.535533906 + 5 Combine like terms: -5 + 5 = 0 0 + y = -3.535533906 + 5 y = -3.535533906 + 5 Combine like terms: -3.535533906 + 5 = 1.464466094 y = 1.464466094 Simplifying y = 1.464466094Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.535533906, 1.464466094}
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