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Simplifying (y2) + -9y + -25 = 0 y2 + -9y + -25 = 0 Reorder the terms: -25 + -9y + y2 = 0 Solving -25 + -9y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -9y + 25 + y2 = 0 + 25 Reorder the terms: -25 + 25 + -9y + y2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -9y + y2 = 0 + 25 -9y + y2 = 0 + 25 Combine like terms: 0 + 25 = 25 -9y + y2 = 25 The y term is -9y. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9y + 20.25 + y2 = 25 + 20.25 Reorder the terms: 20.25 + -9y + y2 = 25 + 20.25 Combine like terms: 25 + 20.25 = 45.25 20.25 + -9y + y2 = 45.25 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (y + -4.5) equal to 6.726812024 and -6.726812024.Subproblem 1
y + -4.5 = 6.726812024 Simplifying y + -4.5 = 6.726812024 Reorder the terms: -4.5 + y = 6.726812024 Solving -4.5 + y = 6.726812024 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = 6.726812024 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 6.726812024 + 4.5 y = 6.726812024 + 4.5 Combine like terms: 6.726812024 + 4.5 = 11.226812024 y = 11.226812024 Simplifying y = 11.226812024Subproblem 2
y + -4.5 = -6.726812024 Simplifying y + -4.5 = -6.726812024 Reorder the terms: -4.5 + y = -6.726812024 Solving -4.5 + y = -6.726812024 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = -6.726812024 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -6.726812024 + 4.5 y = -6.726812024 + 4.5 Combine like terms: -6.726812024 + 4.5 = -2.226812024 y = -2.226812024 Simplifying y = -2.226812024Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.226812024, -2.226812024}
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