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Simplifying 2y4 + -16y2 + 16 = 0 Reorder the terms: 16 + -16y2 + 2y4 = 0 Solving 16 + -16y2 + 2y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -8y2 + y4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -8y2 + y4)' equal to zero and attempt to solve: Simplifying 8 + -8y2 + y4 = 0 Solving 8 + -8y2 + y4 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -8y2 + -8 + y4 = 0 + -8 Reorder the terms: 8 + -8 + -8y2 + y4 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -8y2 + y4 = 0 + -8 -8y2 + y4 = 0 + -8 Combine like terms: 0 + -8 = -8 -8y2 + y4 = -8 The y term is -8y2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y2 + 16 + y4 = -8 + 16 Reorder the terms: 16 + -8y2 + y4 = -8 + 16 Combine like terms: -8 + 16 = 8 16 + -8y2 + y4 = 8 Factor a perfect square on the left side: (y2 + -4)(y2 + -4) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (y2 + -4) equal to 2.828427125 and -2.828427125.Subproblem 1
y2 + -4 = 2.828427125 Simplifying y2 + -4 = 2.828427125 Reorder the terms: -4 + y2 = 2.828427125 Solving -4 + y2 = 2.828427125 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y2 = 2.828427125 + 4 Combine like terms: -4 + 4 = 0 0 + y2 = 2.828427125 + 4 y2 = 2.828427125 + 4 Combine like terms: 2.828427125 + 4 = 6.828427125 y2 = 6.828427125 Simplifying y2 = 6.828427125 Take the square root of each side: y = {-2.61312593, 2.61312593}Subproblem 2
y2 + -4 = -2.828427125 Simplifying y2 + -4 = -2.828427125 Reorder the terms: -4 + y2 = -2.828427125 Solving -4 + y2 = -2.828427125 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y2 = -2.828427125 + 4 Combine like terms: -4 + 4 = 0 0 + y2 = -2.828427125 + 4 y2 = -2.828427125 + 4 Combine like terms: -2.828427125 + 4 = 1.171572875 y2 = 1.171572875 Simplifying y2 = 1.171572875 Take the square root of each side: y = {-1.0823922, 1.0823922}Solution
The solution to the problem is based on the solutions from the subproblems. y = {-2.61312593, 2.61312593, -1.0823922, 1.0823922}Solution
y = {-2.61312593, 2.61312593, -1.0823922, 1.0823922}
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