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Simplifying y2 + -2y + -4 = 16y + -32 Reorder the terms: -4 + -2y + y2 = 16y + -32 Reorder the terms: -4 + -2y + y2 = -32 + 16y Solving -4 + -2y + y2 = -32 + 16y Solving for variable 'y'. Reorder the terms: -4 + 32 + -2y + -16y + y2 = -32 + 16y + 32 + -16y Combine like terms: -4 + 32 = 28 28 + -2y + -16y + y2 = -32 + 16y + 32 + -16y Combine like terms: -2y + -16y = -18y 28 + -18y + y2 = -32 + 16y + 32 + -16y Reorder the terms: 28 + -18y + y2 = -32 + 32 + 16y + -16y Combine like terms: -32 + 32 = 0 28 + -18y + y2 = 0 + 16y + -16y 28 + -18y + y2 = 16y + -16y Combine like terms: 16y + -16y = 0 28 + -18y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -18y + -28 + y2 = 0 + -28 Reorder the terms: 28 + -28 + -18y + y2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -18y + y2 = 0 + -28 -18y + y2 = 0 + -28 Combine like terms: 0 + -28 = -28 -18y + y2 = -28 The y term is -18y. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18y + 81 + y2 = -28 + 81 Reorder the terms: 81 + -18y + y2 = -28 + 81 Combine like terms: -28 + 81 = 53 81 + -18y + y2 = 53 Factor a perfect square on the left side: (y + -9)(y + -9) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (y + -9) equal to 7.280109889 and -7.280109889.Subproblem 1
y + -9 = 7.280109889 Simplifying y + -9 = 7.280109889 Reorder the terms: -9 + y = 7.280109889 Solving -9 + y = 7.280109889 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = 7.280109889 + 9 Combine like terms: -9 + 9 = 0 0 + y = 7.280109889 + 9 y = 7.280109889 + 9 Combine like terms: 7.280109889 + 9 = 16.280109889 y = 16.280109889 Simplifying y = 16.280109889Subproblem 2
y + -9 = -7.280109889 Simplifying y + -9 = -7.280109889 Reorder the terms: -9 + y = -7.280109889 Solving -9 + y = -7.280109889 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = -7.280109889 + 9 Combine like terms: -9 + 9 = 0 0 + y = -7.280109889 + 9 y = -7.280109889 + 9 Combine like terms: -7.280109889 + 9 = 1.719890111 y = 1.719890111 Simplifying y = 1.719890111Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.280109889, 1.719890111}
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