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Simplifying y2 + 7y + -180 = 0 Reorder the terms: -180 + 7y + y2 = 0 Solving -180 + 7y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 7y + 180 + y2 = 0 + 180 Reorder the terms: -180 + 180 + 7y + y2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 7y + y2 = 0 + 180 7y + y2 = 0 + 180 Combine like terms: 0 + 180 = 180 7y + y2 = 180 The y term is 7y. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7y + 12.25 + y2 = 180 + 12.25 Reorder the terms: 12.25 + 7y + y2 = 180 + 12.25 Combine like terms: 180 + 12.25 = 192.25 12.25 + 7y + y2 = 192.25 Factor a perfect square on the left side: (y + 3.5)(y + 3.5) = 192.25 Calculate the square root of the right side: 13.865424624 Break this problem into two subproblems by setting (y + 3.5) equal to 13.865424624 and -13.865424624.Subproblem 1
y + 3.5 = 13.865424624 Simplifying y + 3.5 = 13.865424624 Reorder the terms: 3.5 + y = 13.865424624 Solving 3.5 + y = 13.865424624 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = 13.865424624 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = 13.865424624 + -3.5 y = 13.865424624 + -3.5 Combine like terms: 13.865424624 + -3.5 = 10.365424624 y = 10.365424624 Simplifying y = 10.365424624Subproblem 2
y + 3.5 = -13.865424624 Simplifying y + 3.5 = -13.865424624 Reorder the terms: 3.5 + y = -13.865424624 Solving 3.5 + y = -13.865424624 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + y = -13.865424624 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + y = -13.865424624 + -3.5 y = -13.865424624 + -3.5 Combine like terms: -13.865424624 + -3.5 = -17.365424624 y = -17.365424624 Simplifying y = -17.365424624Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.365424624, -17.365424624}
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