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Simplifying ((y + 8)(y + 8)) + -40 = 0 Reorder the terms: ((8 + y)(y + 8)) + -40 = 0 Reorder the terms: ((8 + y)(8 + y)) + -40 = 0 Multiply (8 + y) * (8 + y) ((8(8 + y) + y(8 + y))) + -40 = 0 (((8 * 8 + y * 8) + y(8 + y))) + -40 = 0 (((64 + 8y) + y(8 + y))) + -40 = 0 ((64 + 8y + (8 * y + y * y))) + -40 = 0 ((64 + 8y + (8y + y2))) + -40 = 0 Combine like terms: 8y + 8y = 16y ((64 + 16y + y2)) + -40 = 0 (64 + 16y + y2) + -40 = 0 Remove parenthesis around (64 + 16y + y2) 64 + 16y + y2 + -40 = 0 Reorder the terms: 64 + -40 + 16y + y2 = 0 Combine like terms: 64 + -40 = 24 24 + 16y + y2 = 0 Solving 24 + 16y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 16y + -24 + y2 = 0 + -24 Reorder the terms: 24 + -24 + 16y + y2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 16y + y2 = 0 + -24 16y + y2 = 0 + -24 Combine like terms: 0 + -24 = -24 16y + y2 = -24 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 = -24 + 64 Reorder the terms: 64 + 16y + y2 = -24 + 64 Combine like terms: -24 + 64 = 40 64 + 16y + y2 = 40 Factor a perfect square on the left side: (y + 8)(y + 8) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (y + 8) equal to 6.32455532 and -6.32455532.Subproblem 1
y + 8 = 6.32455532 Simplifying y + 8 = 6.32455532 Reorder the terms: 8 + y = 6.32455532 Solving 8 + y = 6.32455532 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 = 6.32455532 + -8 Combine like terms: 8 + -8 = 0 0 + y = 6.32455532 + -8 y = 6.32455532 + -8 Combine like terms: 6.32455532 + -8 = -1.67544468 y = -1.67544468 Simplifying y = -1.67544468Subproblem 2
y + 8 = -6.32455532 Simplifying y + 8 = -6.32455532 Reorder the terms: 8 + y = -6.32455532 Solving 8 + y = -6.32455532 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 = -6.32455532 + -8 Combine like terms: 8 + -8 = 0 0 + y = -6.32455532 + -8 y = -6.32455532 + -8 Combine like terms: -6.32455532 + -8 = -14.32455532 y = -14.32455532 Simplifying y = -14.32455532Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.67544468, -14.32455532}
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