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Simplifying y2 + 12y = 7 Reorder the terms: 12y + y2 = 7 Solving 12y + y2 = 7 Solving for variable 'y'. Reorder the terms: -7 + 12y + y2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 12y + 7 + y2 = 0 + 7 Reorder the terms: -7 + 7 + 12y + y2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 12y + y2 = 0 + 7 12y + y2 = 0 + 7 Combine like terms: 0 + 7 = 7 12y + y2 = 7 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 = 7 + 36 Reorder the terms: 36 + 12y + y2 = 7 + 36 Combine like terms: 7 + 36 = 43 36 + 12y + y2 = 43 Factor a perfect square on the left side: (y + 6)(y + 6) = 43 Calculate the square root of the right side: 6.557438524 Break this problem into two subproblems by setting (y + 6) equal to 6.557438524 and -6.557438524.Subproblem 1
y + 6 = 6.557438524 Simplifying y + 6 = 6.557438524 Reorder the terms: 6 + y = 6.557438524 Solving 6 + y = 6.557438524 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 = 6.557438524 + -6 Combine like terms: 6 + -6 = 0 0 + y = 6.557438524 + -6 y = 6.557438524 + -6 Combine like terms: 6.557438524 + -6 = 0.557438524 y = 0.557438524 Simplifying y = 0.557438524Subproblem 2
y + 6 = -6.557438524 Simplifying y + 6 = -6.557438524 Reorder the terms: 6 + y = -6.557438524 Solving 6 + y = -6.557438524 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 = -6.557438524 + -6 Combine like terms: 6 + -6 = 0 0 + y = -6.557438524 + -6 y = -6.557438524 + -6 Combine like terms: -6.557438524 + -6 = -12.557438524 y = -12.557438524 Simplifying y = -12.557438524Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.557438524, -12.557438524}
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