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Simplifying y4 + -18y2 + 73 = 0 Reorder the terms: 73 + -18y2 + y4 = 0 Solving 73 + -18y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-73' to each side of the equation. 73 + -18y2 + -73 + y4 = 0 + -73 Reorder the terms: 73 + -73 + -18y2 + y4 = 0 + -73 Combine like terms: 73 + -73 = 0 0 + -18y2 + y4 = 0 + -73 -18y2 + y4 = 0 + -73 Combine like terms: 0 + -73 = -73 -18y2 + y4 = -73 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 = -73 + 81 Reorder the terms: 81 + -18y2 + y4 = -73 + 81 Combine like terms: -73 + 81 = 8 81 + -18y2 + y4 = 8 Factor a perfect square on the left side: (y2 + -9)(y2 + -9) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (y2 + -9) equal to 2.828427125 and -2.828427125.Subproblem 1
y2 + -9 = 2.828427125 Simplifying y2 + -9 = 2.828427125 Reorder the terms: -9 + y2 = 2.828427125 Solving -9 + y2 = 2.828427125 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 = 2.828427125 + 9 Combine like terms: -9 + 9 = 0 0 + y2 = 2.828427125 + 9 y2 = 2.828427125 + 9 Combine like terms: 2.828427125 + 9 = 11.828427125 y2 = 11.828427125 Simplifying y2 = 11.828427125 Take the square root of each side: y = {-3.439248046, 3.439248046}Subproblem 2
y2 + -9 = -2.828427125 Simplifying y2 + -9 = -2.828427125 Reorder the terms: -9 + y2 = -2.828427125 Solving -9 + y2 = -2.828427125 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 = -2.828427125 + 9 Combine like terms: -9 + 9 = 0 0 + y2 = -2.828427125 + 9 y2 = -2.828427125 + 9 Combine like terms: -2.828427125 + 9 = 6.171572875 y2 = 6.171572875 Simplifying y2 = 6.171572875 Take the square root of each side: y = {-2.484265057, 2.484265057}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-3.439248046, 3.439248046, -2.484265057, 2.484265057}
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