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Simplifying x4 + -20x2 + 92 = 0 Reorder the terms: 92 + -20x2 + x4 = 0 Solving 92 + -20x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-92' to each side of the equation. 92 + -20x2 + -92 + x4 = 0 + -92 Reorder the terms: 92 + -92 + -20x2 + x4 = 0 + -92 Combine like terms: 92 + -92 = 0 0 + -20x2 + x4 = 0 + -92 -20x2 + x4 = 0 + -92 Combine like terms: 0 + -92 = -92 -20x2 + x4 = -92 The x term is -20x2. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x2 + 100 + x4 = -92 + 100 Reorder the terms: 100 + -20x2 + x4 = -92 + 100 Combine like terms: -92 + 100 = 8 100 + -20x2 + x4 = 8 Factor a perfect square on the left side: (x2 + -10)(x2 + -10) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x2 + -10) equal to 2.828427125 and -2.828427125.Subproblem 1
x2 + -10 = 2.828427125 Simplifying x2 + -10 = 2.828427125 Reorder the terms: -10 + x2 = 2.828427125 Solving -10 + x2 = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x2 = 2.828427125 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = 2.828427125 + 10 x2 = 2.828427125 + 10 Combine like terms: 2.828427125 + 10 = 12.828427125 x2 = 12.828427125 Simplifying x2 = 12.828427125 Take the square root of each side: x = {-3.581679372, 3.581679372}Subproblem 2
x2 + -10 = -2.828427125 Simplifying x2 + -10 = -2.828427125 Reorder the terms: -10 + x2 = -2.828427125 Solving -10 + x2 = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x2 = -2.828427125 + 10 Combine like terms: -10 + 10 = 0 0 + x2 = -2.828427125 + 10 x2 = -2.828427125 + 10 Combine like terms: -2.828427125 + 10 = 7.171572875 x2 = 7.171572875 Simplifying x2 = 7.171572875 Take the square root of each side: x = {-2.677979252, 2.677979252}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.581679372, 3.581679372, -2.677979252, 2.677979252}
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