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Simplifying y2 + 14y + -14 = 0 Reorder the terms: -14 + 14y + y2 = 0 Solving -14 + 14y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 14y + 14 + y2 = 0 + 14 Reorder the terms: -14 + 14 + 14y + y2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 14y + y2 = 0 + 14 14y + y2 = 0 + 14 Combine like terms: 0 + 14 = 14 14y + y2 = 14 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 = 14 + 49 Reorder the terms: 49 + 14y + y2 = 14 + 49 Combine like terms: 14 + 49 = 63 49 + 14y + y2 = 63 Factor a perfect square on the left side: (y + 7)(y + 7) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (y + 7) equal to 7.937253933 and -7.937253933.Subproblem 1
y + 7 = 7.937253933 Simplifying y + 7 = 7.937253933 Reorder the terms: 7 + y = 7.937253933 Solving 7 + y = 7.937253933 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 = 7.937253933 + -7 Combine like terms: 7 + -7 = 0 0 + y = 7.937253933 + -7 y = 7.937253933 + -7 Combine like terms: 7.937253933 + -7 = 0.937253933 y = 0.937253933 Simplifying y = 0.937253933Subproblem 2
y + 7 = -7.937253933 Simplifying y + 7 = -7.937253933 Reorder the terms: 7 + y = -7.937253933 Solving 7 + y = -7.937253933 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 = -7.937253933 + -7 Combine like terms: 7 + -7 = 0 0 + y = -7.937253933 + -7 y = -7.937253933 + -7 Combine like terms: -7.937253933 + -7 = -14.937253933 y = -14.937253933 Simplifying y = -14.937253933Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.937253933, -14.937253933}
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