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Simplifying 100 = y2 + 2y + -96 Reorder the terms: 100 = -96 + 2y + y2 Solving 100 = -96 + 2y + y2 Solving for variable 'y'. Combine like terms: 100 + 96 = 196 196 + -2y + -1y2 = -96 + 2y + y2 + 96 + -2y + -1y2 Reorder the terms: 196 + -2y + -1y2 = -96 + 96 + 2y + -2y + y2 + -1y2 Combine like terms: -96 + 96 = 0 196 + -2y + -1y2 = 0 + 2y + -2y + y2 + -1y2 196 + -2y + -1y2 = 2y + -2y + y2 + -1y2 Combine like terms: 2y + -2y = 0 196 + -2y + -1y2 = 0 + y2 + -1y2 196 + -2y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 196 + -2y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -196 + 2y + y2 = 0 Move the constant term to the right: Add '196' to each side of the equation. -196 + 2y + 196 + y2 = 0 + 196 Reorder the terms: -196 + 196 + 2y + y2 = 0 + 196 Combine like terms: -196 + 196 = 0 0 + 2y + y2 = 0 + 196 2y + y2 = 0 + 196 Combine like terms: 0 + 196 = 196 2y + y2 = 196 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = 196 + 1 Reorder the terms: 1 + 2y + y2 = 196 + 1 Combine like terms: 196 + 1 = 197 1 + 2y + y2 = 197 Factor a perfect square on the left side: (y + 1)(y + 1) = 197 Calculate the square root of the right side: 14.035668848 Break this problem into two subproblems by setting (y + 1) equal to 14.035668848 and -14.035668848.Subproblem 1
y + 1 = 14.035668848 Simplifying y + 1 = 14.035668848 Reorder the terms: 1 + y = 14.035668848 Solving 1 + y = 14.035668848 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = 14.035668848 + -1 Combine like terms: 1 + -1 = 0 0 + y = 14.035668848 + -1 y = 14.035668848 + -1 Combine like terms: 14.035668848 + -1 = 13.035668848 y = 13.035668848 Simplifying y = 13.035668848Subproblem 2
y + 1 = -14.035668848 Simplifying y + 1 = -14.035668848 Reorder the terms: 1 + y = -14.035668848 Solving 1 + y = -14.035668848 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + y = -14.035668848 + -1 Combine like terms: 1 + -1 = 0 0 + y = -14.035668848 + -1 y = -14.035668848 + -1 Combine like terms: -14.035668848 + -1 = -15.035668848 y = -15.035668848 Simplifying y = -15.035668848Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.035668848, -15.035668848}
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