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Simplifying y2 + -28y + 36 = 0 Reorder the terms: 36 + -28y + y2 = 0 Solving 36 + -28y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -28y + -36 + y2 = 0 + -36 Reorder the terms: 36 + -36 + -28y + y2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -28y + y2 = 0 + -36 -28y + y2 = 0 + -36 Combine like terms: 0 + -36 = -36 -28y + y2 = -36 The y term is -28y. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28y + 196 + y2 = -36 + 196 Reorder the terms: 196 + -28y + y2 = -36 + 196 Combine like terms: -36 + 196 = 160 196 + -28y + y2 = 160 Factor a perfect square on the left side: (y + -14)(y + -14) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (y + -14) equal to 12.649110641 and -12.649110641.Subproblem 1
y + -14 = 12.649110641 Simplifying y + -14 = 12.649110641 Reorder the terms: -14 + y = 12.649110641 Solving -14 + y = 12.649110641 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + y = 12.649110641 + 14 Combine like terms: -14 + 14 = 0 0 + y = 12.649110641 + 14 y = 12.649110641 + 14 Combine like terms: 12.649110641 + 14 = 26.649110641 y = 26.649110641 Simplifying y = 26.649110641Subproblem 2
y + -14 = -12.649110641 Simplifying y + -14 = -12.649110641 Reorder the terms: -14 + y = -12.649110641 Solving -14 + y = -12.649110641 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + y = -12.649110641 + 14 Combine like terms: -14 + 14 = 0 0 + y = -12.649110641 + 14 y = -12.649110641 + 14 Combine like terms: -12.649110641 + 14 = 1.350889359 y = 1.350889359 Simplifying y = 1.350889359Solution
The solution to the problem is based on the solutions from the subproblems. y = {26.649110641, 1.350889359}
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