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Simplifying y2 + 17y + -6 = 0 Reorder the terms: -6 + 17y + y2 = 0 Solving -6 + 17y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 17y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + 17y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 17y + y2 = 0 + 6 17y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 17y + y2 = 6 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 = 6 + 72.25 Reorder the terms: 72.25 + 17y + y2 = 6 + 72.25 Combine like terms: 6 + 72.25 = 78.25 72.25 + 17y + y2 = 78.25 Factor a perfect square on the left side: (y + 8.5)(y + 8.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (y + 8.5) equal to 8.845903006 and -8.845903006.Subproblem 1
y + 8.5 = 8.845903006 Simplifying y + 8.5 = 8.845903006 Reorder the terms: 8.5 + y = 8.845903006 Solving 8.5 + y = 8.845903006 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 = 8.845903006 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + y = 8.845903006 + -8.5 y = 8.845903006 + -8.5 Combine like terms: 8.845903006 + -8.5 = 0.345903006 y = 0.345903006 Simplifying y = 0.345903006Subproblem 2
y + 8.5 = -8.845903006 Simplifying y + 8.5 = -8.845903006 Reorder the terms: 8.5 + y = -8.845903006 Solving 8.5 + y = -8.845903006 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 = -8.845903006 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + y = -8.845903006 + -8.5 y = -8.845903006 + -8.5 Combine like terms: -8.845903006 + -8.5 = -17.345903006 y = -17.345903006 Simplifying y = -17.345903006Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.345903006, -17.345903006}
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