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Simplifying y2 + 12y + 24 = 0 Reorder the terms: 24 + 12y + y2 = 0 Solving 24 + 12y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 12y + -24 + y2 = 0 + -24 Reorder the terms: 24 + -24 + 12y + y2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 12y + y2 = 0 + -24 12y + y2 = 0 + -24 Combine like terms: 0 + -24 = -24 12y + y2 = -24 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 = -24 + 36 Reorder the terms: 36 + 12y + y2 = -24 + 36 Combine like terms: -24 + 36 = 12 36 + 12y + y2 = 12 Factor a perfect square on the left side: (y + 6)(y + 6) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (y + 6) equal to 3.464101615 and -3.464101615.Subproblem 1
y + 6 = 3.464101615 Simplifying y + 6 = 3.464101615 Reorder the terms: 6 + y = 3.464101615 Solving 6 + y = 3.464101615 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 = 3.464101615 + -6 Combine like terms: 6 + -6 = 0 0 + y = 3.464101615 + -6 y = 3.464101615 + -6 Combine like terms: 3.464101615 + -6 = -2.535898385 y = -2.535898385 Simplifying y = -2.535898385Subproblem 2
y + 6 = -3.464101615 Simplifying y + 6 = -3.464101615 Reorder the terms: 6 + y = -3.464101615 Solving 6 + y = -3.464101615 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 = -3.464101615 + -6 Combine like terms: 6 + -6 = 0 0 + y = -3.464101615 + -6 y = -3.464101615 + -6 Combine like terms: -3.464101615 + -6 = -9.464101615 y = -9.464101615 Simplifying y = -9.464101615Solution
The solution to the problem is based on the solutions from the subproblems. y = {-2.535898385, -9.464101615}
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