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Simplifying y2 + 21y + 36 = 0 Reorder the terms: 36 + 21y + y2 = 0 Solving 36 + 21y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + 21y + -36 + y2 = 0 + -36 Reorder the terms: 36 + -36 + 21y + y2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 21y + y2 = 0 + -36 21y + y2 = 0 + -36 Combine like terms: 0 + -36 = -36 21y + y2 = -36 The y term is 21y. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21y + 110.25 + y2 = -36 + 110.25 Reorder the terms: 110.25 + 21y + y2 = -36 + 110.25 Combine like terms: -36 + 110.25 = 74.25 110.25 + 21y + y2 = 74.25 Factor a perfect square on the left side: (y + 10.5)(y + 10.5) = 74.25 Calculate the square root of the right side: 8.61684397 Break this problem into two subproblems by setting (y + 10.5) equal to 8.61684397 and -8.61684397.Subproblem 1
y + 10.5 = 8.61684397 Simplifying y + 10.5 = 8.61684397 Reorder the terms: 10.5 + y = 8.61684397 Solving 10.5 + y = 8.61684397 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + y = 8.61684397 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + y = 8.61684397 + -10.5 y = 8.61684397 + -10.5 Combine like terms: 8.61684397 + -10.5 = -1.88315603 y = -1.88315603 Simplifying y = -1.88315603Subproblem 2
y + 10.5 = -8.61684397 Simplifying y + 10.5 = -8.61684397 Reorder the terms: 10.5 + y = -8.61684397 Solving 10.5 + y = -8.61684397 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + y = -8.61684397 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + y = -8.61684397 + -10.5 y = -8.61684397 + -10.5 Combine like terms: -8.61684397 + -10.5 = -19.11684397 y = -19.11684397 Simplifying y = -19.11684397Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.88315603, -19.11684397}
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