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Simplifying y2 + 12y + 17 = 0 Reorder the terms: 17 + 12y + y2 = 0 Solving 17 + 12y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 12y + -17 + y2 = 0 + -17 Reorder the terms: 17 + -17 + 12y + y2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 12y + y2 = 0 + -17 12y + y2 = 0 + -17 Combine like terms: 0 + -17 = -17 12y + y2 = -17 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 = -17 + 36 Reorder the terms: 36 + 12y + y2 = -17 + 36 Combine like terms: -17 + 36 = 19 36 + 12y + y2 = 19 Factor a perfect square on the left side: (y + 6)(y + 6) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (y + 6) equal to 4.358898944 and -4.358898944.Subproblem 1
y + 6 = 4.358898944 Simplifying y + 6 = 4.358898944 Reorder the terms: 6 + y = 4.358898944 Solving 6 + y = 4.358898944 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 = 4.358898944 + -6 Combine like terms: 6 + -6 = 0 0 + y = 4.358898944 + -6 y = 4.358898944 + -6 Combine like terms: 4.358898944 + -6 = -1.641101056 y = -1.641101056 Simplifying y = -1.641101056Subproblem 2
y + 6 = -4.358898944 Simplifying y + 6 = -4.358898944 Reorder the terms: 6 + y = -4.358898944 Solving 6 + y = -4.358898944 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 = -4.358898944 + -6 Combine like terms: 6 + -6 = 0 0 + y = -4.358898944 + -6 y = -4.358898944 + -6 Combine like terms: -4.358898944 + -6 = -10.358898944 y = -10.358898944 Simplifying y = -10.358898944Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.641101056, -10.358898944}
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