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Simplifying (y + 8)(y + 8) + -7 = 49 Reorder the terms: (8 + y)(y + 8) + -7 = 49 Reorder the terms: (8 + y)(8 + y) + -7 = 49 Multiply (8 + y) * (8 + y) (8(8 + y) + y(8 + y)) + -7 = 49 ((8 * 8 + y * 8) + y(8 + y)) + -7 = 49 ((64 + 8y) + y(8 + y)) + -7 = 49 (64 + 8y + (8 * y + y * y)) + -7 = 49 (64 + 8y + (8y + y2)) + -7 = 49 Combine like terms: 8y + 8y = 16y (64 + 16y + y2) + -7 = 49 Reorder the terms: 64 + -7 + 16y + y2 = 49 Combine like terms: 64 + -7 = 57 57 + 16y + y2 = 49 Solving 57 + 16y + y2 = 49 Solving for variable 'y'. Reorder the terms: 57 + -49 + 16y + y2 = 49 + -49 Combine like terms: 57 + -49 = 8 8 + 16y + y2 = 49 + -49 Combine like terms: 49 + -49 = 0 8 + 16y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + 16y + -8 + y2 = 0 + -8 Reorder the terms: 8 + -8 + 16y + y2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 16y + y2 = 0 + -8 16y + y2 = 0 + -8 Combine like terms: 0 + -8 = -8 16y + y2 = -8 The y term is 16y. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16y + 64 + y2 = -8 + 64 Reorder the terms: 64 + 16y + y2 = -8 + 64 Combine like terms: -8 + 64 = 56 64 + 16y + y2 = 56 Factor a perfect square on the left side: (y + 8)(y + 8) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (y + 8) equal to 7.483314774 and -7.483314774.Subproblem 1
y + 8 = 7.483314774 Simplifying y + 8 = 7.483314774 Reorder the terms: 8 + y = 7.483314774 Solving 8 + y = 7.483314774 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = 7.483314774 + -8 Combine like terms: 8 + -8 = 0 0 + y = 7.483314774 + -8 y = 7.483314774 + -8 Combine like terms: 7.483314774 + -8 = -0.516685226 y = -0.516685226 Simplifying y = -0.516685226Subproblem 2
y + 8 = -7.483314774 Simplifying y + 8 = -7.483314774 Reorder the terms: 8 + y = -7.483314774 Solving 8 + y = -7.483314774 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + y = -7.483314774 + -8 Combine like terms: 8 + -8 = 0 0 + y = -7.483314774 + -8 y = -7.483314774 + -8 Combine like terms: -7.483314774 + -8 = -15.483314774 y = -15.483314774 Simplifying y = -15.483314774Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.516685226, -15.483314774}
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