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Simplifying y2 + -9y + -88 = 0 Reorder the terms: -88 + -9y + y2 = 0 Solving -88 + -9y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + -9y + 88 + y2 = 0 + 88 Reorder the terms: -88 + 88 + -9y + y2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + -9y + y2 = 0 + 88 -9y + y2 = 0 + 88 Combine like terms: 0 + 88 = 88 -9y + y2 = 88 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 = 88 + 20.25 Reorder the terms: 20.25 + -9y + y2 = 88 + 20.25 Combine like terms: 88 + 20.25 = 108.25 20.25 + -9y + y2 = 108.25 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (y + -4.5) equal to 10.404326023 and -10.404326023.Subproblem 1
y + -4.5 = 10.404326023 Simplifying y + -4.5 = 10.404326023 Reorder the terms: -4.5 + y = 10.404326023 Solving -4.5 + y = 10.404326023 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 = 10.404326023 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 10.404326023 + 4.5 y = 10.404326023 + 4.5 Combine like terms: 10.404326023 + 4.5 = 14.904326023 y = 14.904326023 Simplifying y = 14.904326023Subproblem 2
y + -4.5 = -10.404326023 Simplifying y + -4.5 = -10.404326023 Reorder the terms: -4.5 + y = -10.404326023 Solving -4.5 + y = -10.404326023 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 = -10.404326023 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -10.404326023 + 4.5 y = -10.404326023 + 4.5 Combine like terms: -10.404326023 + 4.5 = -5.904326023 y = -5.904326023 Simplifying y = -5.904326023Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.904326023, -5.904326023}
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