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Simplifying y2 + -5y = 100 Reorder the terms: -5y + y2 = 100 Solving -5y + y2 = 100 Solving for variable 'y'. Reorder the terms: -100 + -5y + y2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + -5y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -5y + 100 + y2 = 0 + 100 Reorder the terms: -100 + 100 + -5y + y2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -5y + y2 = 0 + 100 -5y + y2 = 0 + 100 Combine like terms: 0 + 100 = 100 -5y + y2 = 100 The y term is -5y. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5y + 6.25 + y2 = 100 + 6.25 Reorder the terms: 6.25 + -5y + y2 = 100 + 6.25 Combine like terms: 100 + 6.25 = 106.25 6.25 + -5y + y2 = 106.25 Factor a perfect square on the left side: (y + -2.5)(y + -2.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (y + -2.5) equal to 10.307764064 and -10.307764064.Subproblem 1
y + -2.5 = 10.307764064 Simplifying y + -2.5 = 10.307764064 Reorder the terms: -2.5 + y = 10.307764064 Solving -2.5 + y = 10.307764064 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = 10.307764064 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = 10.307764064 + 2.5 y = 10.307764064 + 2.5 Combine like terms: 10.307764064 + 2.5 = 12.807764064 y = 12.807764064 Simplifying y = 12.807764064Subproblem 2
y + -2.5 = -10.307764064 Simplifying y + -2.5 = -10.307764064 Reorder the terms: -2.5 + y = -10.307764064 Solving -2.5 + y = -10.307764064 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + y = -10.307764064 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + y = -10.307764064 + 2.5 y = -10.307764064 + 2.5 Combine like terms: -10.307764064 + 2.5 = -7.807764064 y = -7.807764064 Simplifying y = -7.807764064Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.807764064, -7.807764064}
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