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Simplifying 100 = y2 + 2y + 4 Reorder the terms: 100 = 4 + 2y + y2 Solving 100 = 4 + 2y + y2 Solving for variable 'y'. Combine like terms: 100 + -4 = 96 96 + -2y + -1y2 = 4 + 2y + y2 + -4 + -2y + -1y2 Reorder the terms: 96 + -2y + -1y2 = 4 + -4 + 2y + -2y + y2 + -1y2 Combine like terms: 4 + -4 = 0 96 + -2y + -1y2 = 0 + 2y + -2y + y2 + -1y2 96 + -2y + -1y2 = 2y + -2y + y2 + -1y2 Combine like terms: 2y + -2y = 0 96 + -2y + -1y2 = 0 + y2 + -1y2 96 + -2y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 96 + -2y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -96 + 2y + y2 = 0 Move the constant term to the right: Add '96' to each side of the equation. -96 + 2y + 96 + y2 = 0 + 96 Reorder the terms: -96 + 96 + 2y + y2 = 0 + 96 Combine like terms: -96 + 96 = 0 0 + 2y + y2 = 0 + 96 2y + y2 = 0 + 96 Combine like terms: 0 + 96 = 96 2y + y2 = 96 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 = 96 + 1 Reorder the terms: 1 + 2y + y2 = 96 + 1 Combine like terms: 96 + 1 = 97 1 + 2y + y2 = 97 Factor a perfect square on the left side: (y + 1)(y + 1) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (y + 1) equal to 9.848857802 and -9.848857802.Subproblem 1
y + 1 = 9.848857802 Simplifying y + 1 = 9.848857802 Reorder the terms: 1 + y = 9.848857802 Solving 1 + y = 9.848857802 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 = 9.848857802 + -1 Combine like terms: 1 + -1 = 0 0 + y = 9.848857802 + -1 y = 9.848857802 + -1 Combine like terms: 9.848857802 + -1 = 8.848857802 y = 8.848857802 Simplifying y = 8.848857802Subproblem 2
y + 1 = -9.848857802 Simplifying y + 1 = -9.848857802 Reorder the terms: 1 + y = -9.848857802 Solving 1 + y = -9.848857802 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 = -9.848857802 + -1 Combine like terms: 1 + -1 = 0 0 + y = -9.848857802 + -1 y = -9.848857802 + -1 Combine like terms: -9.848857802 + -1 = -10.848857802 y = -10.848857802 Simplifying y = -10.848857802Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.848857802, -10.848857802}
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