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Simplifying y(y) + 12y + -36 = 0 Multiply y * y y2 + 12y + -36 = 0 Reorder the terms: -36 + 12y + y2 = 0 Solving -36 + 12y + 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 + 12y + 36 + y2 = 0 + 36 Reorder the terms: -36 + 36 + 12y + y2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 12y + y2 = 0 + 36 12y + y2 = 0 + 36 Combine like terms: 0 + 36 = 36 12y + y2 = 36 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 = 36 + 36 Reorder the terms: 36 + 12y + y2 = 36 + 36 Combine like terms: 36 + 36 = 72 36 + 12y + y2 = 72 Factor a perfect square on the left side: (y + 6)(y + 6) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (y + 6) equal to 8.485281374 and -8.485281374.Subproblem 1
y + 6 = 8.485281374 Simplifying y + 6 = 8.485281374 Reorder the terms: 6 + y = 8.485281374 Solving 6 + y = 8.485281374 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 = 8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + y = 8.485281374 + -6 y = 8.485281374 + -6 Combine like terms: 8.485281374 + -6 = 2.485281374 y = 2.485281374 Simplifying y = 2.485281374Subproblem 2
y + 6 = -8.485281374 Simplifying y + 6 = -8.485281374 Reorder the terms: 6 + y = -8.485281374 Solving 6 + y = -8.485281374 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 = -8.485281374 + -6 Combine like terms: 6 + -6 = 0 0 + y = -8.485281374 + -6 y = -8.485281374 + -6 Combine like terms: -8.485281374 + -6 = -14.485281374 y = -14.485281374 Simplifying y = -14.485281374Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.485281374, -14.485281374}
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