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Simplifying y2 + -12y + -243 = 0 Reorder the terms: -243 + -12y + y2 = 0 Solving -243 + -12y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '243' to each side of the equation. -243 + -12y + 243 + y2 = 0 + 243 Reorder the terms: -243 + 243 + -12y + y2 = 0 + 243 Combine like terms: -243 + 243 = 0 0 + -12y + y2 = 0 + 243 -12y + y2 = 0 + 243 Combine like terms: 0 + 243 = 243 -12y + y2 = 243 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = 243 + 36 Reorder the terms: 36 + -12y + y2 = 243 + 36 Combine like terms: 243 + 36 = 279 36 + -12y + y2 = 279 Factor a perfect square on the left side: (y + -6)(y + -6) = 279 Calculate the square root of the right side: 16.703293088 Break this problem into two subproblems by setting (y + -6) equal to 16.703293088 and -16.703293088.Subproblem 1
y + -6 = 16.703293088 Simplifying y + -6 = 16.703293088 Reorder the terms: -6 + y = 16.703293088 Solving -6 + y = 16.703293088 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 16.703293088 + 6 Combine like terms: -6 + 6 = 0 0 + y = 16.703293088 + 6 y = 16.703293088 + 6 Combine like terms: 16.703293088 + 6 = 22.703293088 y = 22.703293088 Simplifying y = 22.703293088Subproblem 2
y + -6 = -16.703293088 Simplifying y + -6 = -16.703293088 Reorder the terms: -6 + y = -16.703293088 Solving -6 + y = -16.703293088 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -16.703293088 + 6 Combine like terms: -6 + 6 = 0 0 + y = -16.703293088 + 6 y = -16.703293088 + 6 Combine like terms: -16.703293088 + 6 = -10.703293088 y = -10.703293088 Simplifying y = -10.703293088Solution
The solution to the problem is based on the solutions from the subproblems. y = {22.703293088, -10.703293088}
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