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Simplifying (y + 8)(y + 8) + -80 = 0 Reorder the terms: (8 + y)(y + 8) + -80 = 0 Reorder the terms: (8 + y)(8 + y) + -80 = 0 Multiply (8 + y) * (8 + y) (8(8 + y) + y(8 + y)) + -80 = 0 ((8 * 8 + y * 8) + y(8 + y)) + -80 = 0 ((64 + 8y) + y(8 + y)) + -80 = 0 (64 + 8y + (8 * y + y * y)) + -80 = 0 (64 + 8y + (8y + y2)) + -80 = 0 Combine like terms: 8y + 8y = 16y (64 + 16y + y2) + -80 = 0 Reorder the terms: 64 + -80 + 16y + y2 = 0 Combine like terms: 64 + -80 = -16 -16 + 16y + y2 = 0 Solving -16 + 16y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + 16y + 16 + y2 = 0 + 16 Reorder the terms: -16 + 16 + 16y + y2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 16y + y2 = 0 + 16 16y + y2 = 0 + 16 Combine like terms: 0 + 16 = 16 16y + y2 = 16 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 = 16 + 64 Reorder the terms: 64 + 16y + y2 = 16 + 64 Combine like terms: 16 + 64 = 80 64 + 16y + y2 = 80 Factor a perfect square on the left side: (y + 8)(y + 8) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (y + 8) equal to 8.94427191 and -8.94427191.Subproblem 1
y + 8 = 8.94427191 Simplifying y + 8 = 8.94427191 Reorder the terms: 8 + y = 8.94427191 Solving 8 + y = 8.94427191 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 = 8.94427191 + -8 Combine like terms: 8 + -8 = 0 0 + y = 8.94427191 + -8 y = 8.94427191 + -8 Combine like terms: 8.94427191 + -8 = 0.94427191 y = 0.94427191 Simplifying y = 0.94427191Subproblem 2
y + 8 = -8.94427191 Simplifying y + 8 = -8.94427191 Reorder the terms: 8 + y = -8.94427191 Solving 8 + y = -8.94427191 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 = -8.94427191 + -8 Combine like terms: 8 + -8 = 0 0 + y = -8.94427191 + -8 y = -8.94427191 + -8 Combine like terms: -8.94427191 + -8 = -16.94427191 y = -16.94427191 Simplifying y = -16.94427191Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.94427191, -16.94427191}
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