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Simplifying y2 + 17y + 20 = 0 Reorder the terms: 20 + 17y + y2 = 0 Solving 20 + 17y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 17y + -20 + y2 = 0 + -20 Reorder the terms: 20 + -20 + 17y + y2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 17y + y2 = 0 + -20 17y + y2 = 0 + -20 Combine like terms: 0 + -20 = -20 17y + y2 = -20 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 = -20 + 72.25 Reorder the terms: 72.25 + 17y + y2 = -20 + 72.25 Combine like terms: -20 + 72.25 = 52.25 72.25 + 17y + y2 = 52.25 Factor a perfect square on the left side: (y + 8.5)(y + 8.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (y + 8.5) equal to 7.228416147 and -7.228416147.Subproblem 1
y + 8.5 = 7.228416147 Simplifying y + 8.5 = 7.228416147 Reorder the terms: 8.5 + y = 7.228416147 Solving 8.5 + y = 7.228416147 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 = 7.228416147 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + y = 7.228416147 + -8.5 y = 7.228416147 + -8.5 Combine like terms: 7.228416147 + -8.5 = -1.271583853 y = -1.271583853 Simplifying y = -1.271583853Subproblem 2
y + 8.5 = -7.228416147 Simplifying y + 8.5 = -7.228416147 Reorder the terms: 8.5 + y = -7.228416147 Solving 8.5 + y = -7.228416147 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 = -7.228416147 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + y = -7.228416147 + -8.5 y = -7.228416147 + -8.5 Combine like terms: -7.228416147 + -8.5 = -15.728416147 y = -15.728416147 Simplifying y = -15.728416147Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.271583853, -15.728416147}
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