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Simplifying x4 + -180x2 + 16 = 0 Reorder the terms: 16 + -180x2 + x4 = 0 Solving 16 + -180x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -180x2 + -16 + x4 = 0 + -16 Reorder the terms: 16 + -16 + -180x2 + x4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -180x2 + x4 = 0 + -16 -180x2 + x4 = 0 + -16 Combine like terms: 0 + -16 = -16 -180x2 + x4 = -16 The x term is -180x2. Take half its coefficient (-90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. -180x2 + 8100 + x4 = -16 + 8100 Reorder the terms: 8100 + -180x2 + x4 = -16 + 8100 Combine like terms: -16 + 8100 = 8084 8100 + -180x2 + x4 = 8084 Factor a perfect square on the left side: (x2 + -90)(x2 + -90) = 8084 Calculate the square root of the right side: 89.911067172 Break this problem into two subproblems by setting (x2 + -90) equal to 89.911067172 and -89.911067172.Subproblem 1
x2 + -90 = 89.911067172 Simplifying x2 + -90 = 89.911067172 Reorder the terms: -90 + x2 = 89.911067172 Solving -90 + x2 = 89.911067172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x2 = 89.911067172 + 90 Combine like terms: -90 + 90 = 0 0 + x2 = 89.911067172 + 90 x2 = 89.911067172 + 90 Combine like terms: 89.911067172 + 90 = 179.911067172 x2 = 179.911067172 Simplifying x2 = 179.911067172 Take the square root of each side: x = {-13.413093125, 13.413093125}Subproblem 2
x2 + -90 = -89.911067172 Simplifying x2 + -90 = -89.911067172 Reorder the terms: -90 + x2 = -89.911067172 Solving -90 + x2 = -89.911067172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x2 = -89.911067172 + 90 Combine like terms: -90 + 90 = 0 0 + x2 = -89.911067172 + 90 x2 = -89.911067172 + 90 Combine like terms: -89.911067172 + 90 = 0.088932828 x2 = 0.088932828 Simplifying x2 = 0.088932828 Take the square root of each side: x = {-0.298216076, 0.298216076}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-13.413093125, 13.413093125, -0.298216076, 0.298216076}
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