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Simplifying y2 + 12y = 15 Reorder the terms: 12y + y2 = 15 Solving 12y + y2 = 15 Solving for variable 'y'. Reorder the terms: -15 + 12y + y2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 12y + 15 + y2 = 0 + 15 Reorder the terms: -15 + 15 + 12y + y2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 12y + y2 = 0 + 15 12y + y2 = 0 + 15 Combine like terms: 0 + 15 = 15 12y + y2 = 15 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 = 15 + 36 Reorder the terms: 36 + 12y + y2 = 15 + 36 Combine like terms: 15 + 36 = 51 36 + 12y + y2 = 51 Factor a perfect square on the left side: (y + 6)(y + 6) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (y + 6) equal to 7.141428429 and -7.141428429.Subproblem 1
y + 6 = 7.141428429 Simplifying y + 6 = 7.141428429 Reorder the terms: 6 + y = 7.141428429 Solving 6 + y = 7.141428429 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 = 7.141428429 + -6 Combine like terms: 6 + -6 = 0 0 + y = 7.141428429 + -6 y = 7.141428429 + -6 Combine like terms: 7.141428429 + -6 = 1.141428429 y = 1.141428429 Simplifying y = 1.141428429Subproblem 2
y + 6 = -7.141428429 Simplifying y + 6 = -7.141428429 Reorder the terms: 6 + y = -7.141428429 Solving 6 + y = -7.141428429 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 = -7.141428429 + -6 Combine like terms: 6 + -6 = 0 0 + y = -7.141428429 + -6 y = -7.141428429 + -6 Combine like terms: -7.141428429 + -6 = -13.141428429 y = -13.141428429 Simplifying y = -13.141428429Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.141428429, -13.141428429}
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