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Simplifying y2 + -28y + 44 = 0 Reorder the terms: 44 + -28y + y2 = 0 Solving 44 + -28y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-44' to each side of the equation. 44 + -28y + -44 + y2 = 0 + -44 Reorder the terms: 44 + -44 + -28y + y2 = 0 + -44 Combine like terms: 44 + -44 = 0 0 + -28y + y2 = 0 + -44 -28y + y2 = 0 + -44 Combine like terms: 0 + -44 = -44 -28y + y2 = -44 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 = -44 + 196 Reorder the terms: 196 + -28y + y2 = -44 + 196 Combine like terms: -44 + 196 = 152 196 + -28y + y2 = 152 Factor a perfect square on the left side: (y + -14)(y + -14) = 152 Calculate the square root of the right side: 12.328828006 Break this problem into two subproblems by setting (y + -14) equal to 12.328828006 and -12.328828006.Subproblem 1
y + -14 = 12.328828006 Simplifying y + -14 = 12.328828006 Reorder the terms: -14 + y = 12.328828006 Solving -14 + y = 12.328828006 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 = 12.328828006 + 14 Combine like terms: -14 + 14 = 0 0 + y = 12.328828006 + 14 y = 12.328828006 + 14 Combine like terms: 12.328828006 + 14 = 26.328828006 y = 26.328828006 Simplifying y = 26.328828006Subproblem 2
y + -14 = -12.328828006 Simplifying y + -14 = -12.328828006 Reorder the terms: -14 + y = -12.328828006 Solving -14 + y = -12.328828006 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 = -12.328828006 + 14 Combine like terms: -14 + 14 = 0 0 + y = -12.328828006 + 14 y = -12.328828006 + 14 Combine like terms: -12.328828006 + 14 = 1.671171994 y = 1.671171994 Simplifying y = 1.671171994Solution
The solution to the problem is based on the solutions from the subproblems. y = {26.328828006, 1.671171994}
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