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Simplifying y2 + 23 = 12y Reorder the terms: 23 + y2 = 12y Solving 23 + y2 = 12y Solving for variable 'y'. Reorder the terms: 23 + -12y + y2 = 12y + -12y Combine like terms: 12y + -12y = 0 23 + -12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + -12y + -23 + y2 = 0 + -23 Reorder the terms: 23 + -23 + -12y + y2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -12y + y2 = 0 + -23 -12y + y2 = 0 + -23 Combine like terms: 0 + -23 = -23 -12y + y2 = -23 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 = -23 + 36 Reorder the terms: 36 + -12y + y2 = -23 + 36 Combine like terms: -23 + 36 = 13 36 + -12y + y2 = 13 Factor a perfect square on the left side: (y + -6)(y + -6) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (y + -6) equal to 3.605551275 and -3.605551275.Subproblem 1
y + -6 = 3.605551275 Simplifying y + -6 = 3.605551275 Reorder the terms: -6 + y = 3.605551275 Solving -6 + y = 3.605551275 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 = 3.605551275 + 6 Combine like terms: -6 + 6 = 0 0 + y = 3.605551275 + 6 y = 3.605551275 + 6 Combine like terms: 3.605551275 + 6 = 9.605551275 y = 9.605551275 Simplifying y = 9.605551275Subproblem 2
y + -6 = -3.605551275 Simplifying y + -6 = -3.605551275 Reorder the terms: -6 + y = -3.605551275 Solving -6 + y = -3.605551275 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 = -3.605551275 + 6 Combine like terms: -6 + 6 = 0 0 + y = -3.605551275 + 6 y = -3.605551275 + 6 Combine like terms: -3.605551275 + 6 = 2.394448725 y = 2.394448725 Simplifying y = 2.394448725Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.605551275, 2.394448725}
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