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Simplifying y4 + -18y2 + 18 = 0 Reorder the terms: 18 + -18y2 + y4 = 0 Solving 18 + -18y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -18y2 + -18 + y4 = 0 + -18 Reorder the terms: 18 + -18 + -18y2 + y4 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -18y2 + y4 = 0 + -18 -18y2 + y4 = 0 + -18 Combine like terms: 0 + -18 = -18 -18y2 + y4 = -18 The y term is -18y2. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18y2 + 81 + y4 = -18 + 81 Reorder the terms: 81 + -18y2 + y4 = -18 + 81 Combine like terms: -18 + 81 = 63 81 + -18y2 + y4 = 63 Factor a perfect square on the left side: (y2 + -9)(y2 + -9) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (y2 + -9) equal to 7.937253933 and -7.937253933.Subproblem 1
y2 + -9 = 7.937253933 Simplifying y2 + -9 = 7.937253933 Reorder the terms: -9 + y2 = 7.937253933 Solving -9 + y2 = 7.937253933 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 + y2 = 7.937253933 + 9 Combine like terms: -9 + 9 = 0 0 + y2 = 7.937253933 + 9 y2 = 7.937253933 + 9 Combine like terms: 7.937253933 + 9 = 16.937253933 y2 = 16.937253933 Simplifying y2 = 16.937253933 Take the square root of each side: y = {-4.115489513, 4.115489513}Subproblem 2
y2 + -9 = -7.937253933 Simplifying y2 + -9 = -7.937253933 Reorder the terms: -9 + y2 = -7.937253933 Solving -9 + y2 = -7.937253933 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 + y2 = -7.937253933 + 9 Combine like terms: -9 + 9 = 0 0 + y2 = -7.937253933 + 9 y2 = -7.937253933 + 9 Combine like terms: -7.937253933 + 9 = 1.062746067 y2 = 1.062746067 Simplifying y2 = 1.062746067 Take the square root of each side: y = {-1.03089576, 1.03089576}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-4.115489513, 4.115489513, -1.03089576, 1.03089576}
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