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Simplifying y2 + -28y + 64 = 0 Reorder the terms: 64 + -28y + y2 = 0 Solving 64 + -28y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + -28y + -64 + y2 = 0 + -64 Reorder the terms: 64 + -64 + -28y + y2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -28y + y2 = 0 + -64 -28y + y2 = 0 + -64 Combine like terms: 0 + -64 = -64 -28y + y2 = -64 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 = -64 + 196 Reorder the terms: 196 + -28y + y2 = -64 + 196 Combine like terms: -64 + 196 = 132 196 + -28y + y2 = 132 Factor a perfect square on the left side: (y + -14)(y + -14) = 132 Calculate the square root of the right side: 11.489125293 Break this problem into two subproblems by setting (y + -14) equal to 11.489125293 and -11.489125293.Subproblem 1
y + -14 = 11.489125293 Simplifying y + -14 = 11.489125293 Reorder the terms: -14 + y = 11.489125293 Solving -14 + y = 11.489125293 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 = 11.489125293 + 14 Combine like terms: -14 + 14 = 0 0 + y = 11.489125293 + 14 y = 11.489125293 + 14 Combine like terms: 11.489125293 + 14 = 25.489125293 y = 25.489125293 Simplifying y = 25.489125293Subproblem 2
y + -14 = -11.489125293 Simplifying y + -14 = -11.489125293 Reorder the terms: -14 + y = -11.489125293 Solving -14 + y = -11.489125293 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 = -11.489125293 + 14 Combine like terms: -14 + 14 = 0 0 + y = -11.489125293 + 14 y = -11.489125293 + 14 Combine like terms: -11.489125293 + 14 = 2.510874707 y = 2.510874707 Simplifying y = 2.510874707Solution
The solution to the problem is based on the solutions from the subproblems. y = {25.489125293, 2.510874707}
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