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Simplifying 0 = -1y2 + 28y + 98 Reorder the terms: 0 = 98 + 28y + -1y2 Solving 0 = 98 + 28y + -1y2 Solving for variable 'y'. Combine like terms: 0 + -98 = -98 -98 + -28y + y2 = 98 + 28y + -1y2 + -98 + -28y + y2 Reorder the terms: -98 + -28y + y2 = 98 + -98 + 28y + -28y + -1y2 + y2 Combine like terms: 98 + -98 = 0 -98 + -28y + y2 = 0 + 28y + -28y + -1y2 + y2 -98 + -28y + y2 = 28y + -28y + -1y2 + y2 Combine like terms: 28y + -28y = 0 -98 + -28y + y2 = 0 + -1y2 + y2 -98 + -28y + y2 = -1y2 + y2 Combine like terms: -1y2 + y2 = 0 -98 + -28y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + -28y + 98 + y2 = 0 + 98 Reorder the terms: -98 + 98 + -28y + y2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -28y + y2 = 0 + 98 -28y + y2 = 0 + 98 Combine like terms: 0 + 98 = 98 -28y + y2 = 98 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 = 98 + 196 Reorder the terms: 196 + -28y + y2 = 98 + 196 Combine like terms: 98 + 196 = 294 196 + -28y + y2 = 294 Factor a perfect square on the left side: (y + -14)(y + -14) = 294 Calculate the square root of the right side: 17.146428199 Break this problem into two subproblems by setting (y + -14) equal to 17.146428199 and -17.146428199.Subproblem 1
y + -14 = 17.146428199 Simplifying y + -14 = 17.146428199 Reorder the terms: -14 + y = 17.146428199 Solving -14 + y = 17.146428199 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 = 17.146428199 + 14 Combine like terms: -14 + 14 = 0 0 + y = 17.146428199 + 14 y = 17.146428199 + 14 Combine like terms: 17.146428199 + 14 = 31.146428199 y = 31.146428199 Simplifying y = 31.146428199Subproblem 2
y + -14 = -17.146428199 Simplifying y + -14 = -17.146428199 Reorder the terms: -14 + y = -17.146428199 Solving -14 + y = -17.146428199 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 = -17.146428199 + 14 Combine like terms: -14 + 14 = 0 0 + y = -17.146428199 + 14 y = -17.146428199 + 14 Combine like terms: -17.146428199 + 14 = -3.146428199 y = -3.146428199 Simplifying y = -3.146428199Solution
The solution to the problem is based on the solutions from the subproblems. y = {31.146428199, -3.146428199}
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