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Simplifying y2 + -10y + -35 = 0 Reorder the terms: -35 + -10y + y2 = 0 Solving -35 + -10y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -10y + 35 + y2 = 0 + 35 Reorder the terms: -35 + 35 + -10y + y2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -10y + y2 = 0 + 35 -10y + y2 = 0 + 35 Combine like terms: 0 + 35 = 35 -10y + y2 = 35 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 = 35 + 25 Reorder the terms: 25 + -10y + y2 = 35 + 25 Combine like terms: 35 + 25 = 60 25 + -10y + y2 = 60 Factor a perfect square on the left side: (y + -5)(y + -5) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (y + -5) equal to 7.745966692 and -7.745966692.Subproblem 1
y + -5 = 7.745966692 Simplifying y + -5 = 7.745966692 Reorder the terms: -5 + y = 7.745966692 Solving -5 + y = 7.745966692 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 = 7.745966692 + 5 Combine like terms: -5 + 5 = 0 0 + y = 7.745966692 + 5 y = 7.745966692 + 5 Combine like terms: 7.745966692 + 5 = 12.745966692 y = 12.745966692 Simplifying y = 12.745966692Subproblem 2
y + -5 = -7.745966692 Simplifying y + -5 = -7.745966692 Reorder the terms: -5 + y = -7.745966692 Solving -5 + y = -7.745966692 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 = -7.745966692 + 5 Combine like terms: -5 + 5 = 0 0 + y = -7.745966692 + 5 y = -7.745966692 + 5 Combine like terms: -7.745966692 + 5 = -2.745966692 y = -2.745966692 Simplifying y = -2.745966692Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.745966692, -2.745966692}
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