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Simplifying y2 + -12y + 14 = 0 Reorder the terms: 14 + -12y + y2 = 0 Solving 14 + -12y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -12y + -14 + y2 = 0 + -14 Reorder the terms: 14 + -14 + -12y + y2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -12y + y2 = 0 + -14 -12y + y2 = 0 + -14 Combine like terms: 0 + -14 = -14 -12y + y2 = -14 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 = -14 + 36 Reorder the terms: 36 + -12y + y2 = -14 + 36 Combine like terms: -14 + 36 = 22 36 + -12y + y2 = 22 Factor a perfect square on the left side: (y + -6)(y + -6) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (y + -6) equal to 4.69041576 and -4.69041576.Subproblem 1
y + -6 = 4.69041576 Simplifying y + -6 = 4.69041576 Reorder the terms: -6 + y = 4.69041576 Solving -6 + y = 4.69041576 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 = 4.69041576 + 6 Combine like terms: -6 + 6 = 0 0 + y = 4.69041576 + 6 y = 4.69041576 + 6 Combine like terms: 4.69041576 + 6 = 10.69041576 y = 10.69041576 Simplifying y = 10.69041576Subproblem 2
y + -6 = -4.69041576 Simplifying y + -6 = -4.69041576 Reorder the terms: -6 + y = -4.69041576 Solving -6 + y = -4.69041576 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 = -4.69041576 + 6 Combine like terms: -6 + 6 = 0 0 + y = -4.69041576 + 6 y = -4.69041576 + 6 Combine like terms: -4.69041576 + 6 = 1.30958424 y = 1.30958424 Simplifying y = 1.30958424Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.69041576, 1.30958424}
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