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Simplifying x4 + -8x2 + -10 = 0 Reorder the terms: -10 + -8x2 + x4 = 0 Solving -10 + -8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -8x2 + 10 + x4 = 0 + 10 Reorder the terms: -10 + 10 + -8x2 + x4 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -8x2 + x4 = 0 + 10 -8x2 + x4 = 0 + 10 Combine like terms: 0 + 10 = 10 -8x2 + x4 = 10 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = 10 + 16 Reorder the terms: 16 + -8x2 + x4 = 10 + 16 Combine like terms: 10 + 16 = 26 16 + -8x2 + x4 = 26 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x2 + -4) equal to 5.099019514 and -5.099019514.Subproblem 1
x2 + -4 = 5.099019514 Simplifying x2 + -4 = 5.099019514 Reorder the terms: -4 + x2 = 5.099019514 Solving -4 + x2 = 5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 5.099019514 + 4 x2 = 5.099019514 + 4 Combine like terms: 5.099019514 + 4 = 9.099019514 x2 = 9.099019514 Simplifying x2 = 9.099019514 Take the square root of each side: x = {-3.016458107, 3.016458107}Subproblem 2
x2 + -4 = -5.099019514 Simplifying x2 + -4 = -5.099019514 Reorder the terms: -4 + x2 = -5.099019514 Solving -4 + x2 = -5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -5.099019514 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -5.099019514 + 4 x2 = -5.099019514 + 4 Combine like terms: -5.099019514 + 4 = -1.099019514 x2 = -1.099019514 Simplifying x2 = -1.099019514 Reorder the terms: 1.099019514 + x2 = -1.099019514 + 1.099019514 Combine like terms: -1.099019514 + 1.099019514 = 0.000000000 1.099019514 + 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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