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Simplifying 49 + -14y + -1y2 = 0 Solving 49 + -14y + -1y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -49 + 14y + y2 = 0 Move the constant term to the right: Add '49' to each side of the equation. -49 + 14y + 49 + y2 = 0 + 49 Reorder the terms: -49 + 49 + 14y + y2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 14y + y2 = 0 + 49 14y + y2 = 0 + 49 Combine like terms: 0 + 49 = 49 14y + y2 = 49 The y term is 14y. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14y + 49 + y2 = 49 + 49 Reorder the terms: 49 + 14y + y2 = 49 + 49 Combine like terms: 49 + 49 = 98 49 + 14y + y2 = 98 Factor a perfect square on the left side: (y + 7)(y + 7) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (y + 7) equal to 9.899494937 and -9.899494937.Subproblem 1
y + 7 = 9.899494937 Simplifying y + 7 = 9.899494937 Reorder the terms: 7 + y = 9.899494937 Solving 7 + y = 9.899494937 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = 9.899494937 + -7 Combine like terms: 7 + -7 = 0 0 + y = 9.899494937 + -7 y = 9.899494937 + -7 Combine like terms: 9.899494937 + -7 = 2.899494937 y = 2.899494937 Simplifying y = 2.899494937Subproblem 2
y + 7 = -9.899494937 Simplifying y + 7 = -9.899494937 Reorder the terms: 7 + y = -9.899494937 Solving 7 + y = -9.899494937 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + y = -9.899494937 + -7 Combine like terms: 7 + -7 = 0 0 + y = -9.899494937 + -7 y = -9.899494937 + -7 Combine like terms: -9.899494937 + -7 = -16.899494937 y = -16.899494937 Simplifying y = -16.899494937Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.899494937, -16.899494937}
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