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Simplifying y2 + -17y + 55 = 0 Reorder the terms: 55 + -17y + y2 = 0 Solving 55 + -17y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-55' to each side of the equation. 55 + -17y + -55 + y2 = 0 + -55 Reorder the terms: 55 + -55 + -17y + y2 = 0 + -55 Combine like terms: 55 + -55 = 0 0 + -17y + y2 = 0 + -55 -17y + y2 = 0 + -55 Combine like terms: 0 + -55 = -55 -17y + y2 = -55 The y term is -17y. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17y + 72.25 + y2 = -55 + 72.25 Reorder the terms: 72.25 + -17y + y2 = -55 + 72.25 Combine like terms: -55 + 72.25 = 17.25 72.25 + -17y + y2 = 17.25 Factor a perfect square on the left side: (y + -8.5)(y + -8.5) = 17.25 Calculate the square root of the right side: 4.153311931 Break this problem into two subproblems by setting (y + -8.5) equal to 4.153311931 and -4.153311931.Subproblem 1
y + -8.5 = 4.153311931 Simplifying y + -8.5 = 4.153311931 Reorder the terms: -8.5 + y = 4.153311931 Solving -8.5 + y = 4.153311931 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + y = 4.153311931 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + y = 4.153311931 + 8.5 y = 4.153311931 + 8.5 Combine like terms: 4.153311931 + 8.5 = 12.653311931 y = 12.653311931 Simplifying y = 12.653311931Subproblem 2
y + -8.5 = -4.153311931 Simplifying y + -8.5 = -4.153311931 Reorder the terms: -8.5 + y = -4.153311931 Solving -8.5 + y = -4.153311931 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + y = -4.153311931 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + y = -4.153311931 + 8.5 y = -4.153311931 + 8.5 Combine like terms: -4.153311931 + 8.5 = 4.346688069 y = 4.346688069 Simplifying y = 4.346688069Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.653311931, 4.346688069}
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