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Simplifying (y + 7)(y + 7) + 5 = 95 Reorder the terms: (7 + y)(y + 7) + 5 = 95 Reorder the terms: (7 + y)(7 + y) + 5 = 95 Multiply (7 + y) * (7 + y) (7(7 + y) + y(7 + y)) + 5 = 95 ((7 * 7 + y * 7) + y(7 + y)) + 5 = 95 ((49 + 7y) + y(7 + y)) + 5 = 95 (49 + 7y + (7 * y + y * y)) + 5 = 95 (49 + 7y + (7y + y2)) + 5 = 95 Combine like terms: 7y + 7y = 14y (49 + 14y + y2) + 5 = 95 Reorder the terms: 49 + 5 + 14y + y2 = 95 Combine like terms: 49 + 5 = 54 54 + 14y + y2 = 95 Solving 54 + 14y + y2 = 95 Solving for variable 'y'. Reorder the terms: 54 + -95 + 14y + y2 = 95 + -95 Combine like terms: 54 + -95 = -41 -41 + 14y + y2 = 95 + -95 Combine like terms: 95 + -95 = 0 -41 + 14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '41' to each side of the equation. -41 + 14y + 41 + y2 = 0 + 41 Reorder the terms: -41 + 41 + 14y + y2 = 0 + 41 Combine like terms: -41 + 41 = 0 0 + 14y + y2 = 0 + 41 14y + y2 = 0 + 41 Combine like terms: 0 + 41 = 41 14y + y2 = 41 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 = 41 + 49 Reorder the terms: 49 + 14y + y2 = 41 + 49 Combine like terms: 41 + 49 = 90 49 + 14y + y2 = 90 Factor a perfect square on the left side: (y + 7)(y + 7) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (y + 7) equal to 9.486832981 and -9.486832981.Subproblem 1
y + 7 = 9.486832981 Simplifying y + 7 = 9.486832981 Reorder the terms: 7 + y = 9.486832981 Solving 7 + y = 9.486832981 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 = 9.486832981 + -7 Combine like terms: 7 + -7 = 0 0 + y = 9.486832981 + -7 y = 9.486832981 + -7 Combine like terms: 9.486832981 + -7 = 2.486832981 y = 2.486832981 Simplifying y = 2.486832981Subproblem 2
y + 7 = -9.486832981 Simplifying y + 7 = -9.486832981 Reorder the terms: 7 + y = -9.486832981 Solving 7 + y = -9.486832981 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 = -9.486832981 + -7 Combine like terms: 7 + -7 = 0 0 + y = -9.486832981 + -7 y = -9.486832981 + -7 Combine like terms: -9.486832981 + -7 = -16.486832981 y = -16.486832981 Simplifying y = -16.486832981Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.486832981, -16.486832981}
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