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Simplifying y(y + 14) = 48 Reorder the terms: y(14 + y) = 48 (14 * y + y * y) = 48 (14y + y2) = 48 Solving 14y + y2 = 48 Solving for variable 'y'. Reorder the terms: -48 + 14y + y2 = 48 + -48 Combine like terms: 48 + -48 = 0 -48 + 14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 14y + 48 + y2 = 0 + 48 Reorder the terms: -48 + 48 + 14y + y2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 14y + y2 = 0 + 48 14y + y2 = 0 + 48 Combine like terms: 0 + 48 = 48 14y + y2 = 48 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 = 48 + 49 Reorder the terms: 49 + 14y + y2 = 48 + 49 Combine like terms: 48 + 49 = 97 49 + 14y + y2 = 97 Factor a perfect square on the left side: (y + 7)(y + 7) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (y + 7) equal to 9.848857802 and -9.848857802.Subproblem 1
y + 7 = 9.848857802 Simplifying y + 7 = 9.848857802 Reorder the terms: 7 + y = 9.848857802 Solving 7 + y = 9.848857802 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 = 9.848857802 + -7 Combine like terms: 7 + -7 = 0 0 + y = 9.848857802 + -7 y = 9.848857802 + -7 Combine like terms: 9.848857802 + -7 = 2.848857802 y = 2.848857802 Simplifying y = 2.848857802Subproblem 2
y + 7 = -9.848857802 Simplifying y + 7 = -9.848857802 Reorder the terms: 7 + y = -9.848857802 Solving 7 + y = -9.848857802 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 = -9.848857802 + -7 Combine like terms: 7 + -7 = 0 0 + y = -9.848857802 + -7 y = -9.848857802 + -7 Combine like terms: -9.848857802 + -7 = -16.848857802 y = -16.848857802 Simplifying y = -16.848857802Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.848857802, -16.848857802}
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