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Simplifying x4 + 2x2 + -25 = 0 Reorder the terms: -25 + 2x2 + x4 = 0 Solving -25 + 2x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 2x2 + 25 + x4 = 0 + 25 Reorder the terms: -25 + 25 + 2x2 + x4 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 2x2 + x4 = 0 + 25 2x2 + x4 = 0 + 25 Combine like terms: 0 + 25 = 25 2x2 + x4 = 25 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = 25 + 1 Reorder the terms: 1 + 2x2 + x4 = 25 + 1 Combine like terms: 25 + 1 = 26 1 + 2x2 + x4 = 26 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x2 + 1) equal to 5.099019514 and -5.099019514.Subproblem 1
x2 + 1 = 5.099019514 Simplifying x2 + 1 = 5.099019514 Reorder the terms: 1 + x2 = 5.099019514 Solving 1 + x2 = 5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = 5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = 5.099019514 + -1 x2 = 5.099019514 + -1 Combine like terms: 5.099019514 + -1 = 4.099019514 x2 = 4.099019514 Simplifying x2 = 4.099019514 Take the square root of each side: x = {-2.024603545, 2.024603545}Subproblem 2
x2 + 1 = -5.099019514 Simplifying x2 + 1 = -5.099019514 Reorder the terms: 1 + x2 = -5.099019514 Solving 1 + x2 = -5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x2 = -5.099019514 + -1 Combine like terms: 1 + -1 = 0 0 + x2 = -5.099019514 + -1 x2 = -5.099019514 + -1 Combine like terms: -5.099019514 + -1 = -6.099019514 x2 = -6.099019514 Simplifying x2 = -6.099019514 Reorder the terms: 6.099019514 + x2 = -6.099019514 + 6.099019514 Combine like terms: -6.099019514 + 6.099019514 = 0.000000000 6.099019514 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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