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Simplifying x4 + -4x2 + -13 = 0 Reorder the terms: -13 + -4x2 + x4 = 0 Solving -13 + -4x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -4x2 + 13 + x4 = 0 + 13 Reorder the terms: -13 + 13 + -4x2 + x4 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -4x2 + x4 = 0 + 13 -4x2 + x4 = 0 + 13 Combine like terms: 0 + 13 = 13 -4x2 + x4 = 13 The x term is -4x2. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x2 + 4 + x4 = 13 + 4 Reorder the terms: 4 + -4x2 + x4 = 13 + 4 Combine like terms: 13 + 4 = 17 4 + -4x2 + x4 = 17 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x2 + -2) equal to 4.123105626 and -4.123105626.Subproblem 1
x2 + -2 = 4.123105626 Simplifying x2 + -2 = 4.123105626 Reorder the terms: -2 + x2 = 4.123105626 Solving -2 + x2 = 4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = 4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 4.123105626 + 2 x2 = 4.123105626 + 2 Combine like terms: 4.123105626 + 2 = 6.123105626 x2 = 6.123105626 Simplifying x2 = 6.123105626 Take the square root of each side: x = {-2.474490983, 2.474490983}Subproblem 2
x2 + -2 = -4.123105626 Simplifying x2 + -2 = -4.123105626 Reorder the terms: -2 + x2 = -4.123105626 Solving -2 + x2 = -4.123105626 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = -4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -4.123105626 + 2 x2 = -4.123105626 + 2 Combine like terms: -4.123105626 + 2 = -2.123105626 x2 = -2.123105626 Simplifying x2 = -2.123105626 Reorder the terms: 2.123105626 + x2 = -2.123105626 + 2.123105626 Combine like terms: -2.123105626 + 2.123105626 = 0.000000000 2.123105626 + 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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