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Simplifying y2 + 9y + -18 = 0 Reorder the terms: -18 + 9y + y2 = 0 Solving -18 + 9y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + 9y + 18 + y2 = 0 + 18 Reorder the terms: -18 + 18 + 9y + y2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 9y + y2 = 0 + 18 9y + y2 = 0 + 18 Combine like terms: 0 + 18 = 18 9y + y2 = 18 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 = 18 + 20.25 Reorder the terms: 20.25 + 9y + y2 = 18 + 20.25 Combine like terms: 18 + 20.25 = 38.25 20.25 + 9y + y2 = 38.25 Factor a perfect square on the left side: (y + 4.5)(y + 4.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (y + 4.5) equal to 6.184658438 and -6.184658438.Subproblem 1
y + 4.5 = 6.184658438 Simplifying y + 4.5 = 6.184658438 Reorder the terms: 4.5 + y = 6.184658438 Solving 4.5 + y = 6.184658438 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 = 6.184658438 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = 6.184658438 + -4.5 y = 6.184658438 + -4.5 Combine like terms: 6.184658438 + -4.5 = 1.684658438 y = 1.684658438 Simplifying y = 1.684658438Subproblem 2
y + 4.5 = -6.184658438 Simplifying y + 4.5 = -6.184658438 Reorder the terms: 4.5 + y = -6.184658438 Solving 4.5 + y = -6.184658438 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 = -6.184658438 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + y = -6.184658438 + -4.5 y = -6.184658438 + -4.5 Combine like terms: -6.184658438 + -4.5 = -10.684658438 y = -10.684658438 Simplifying y = -10.684658438Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.684658438, -10.684658438}
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