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Simplifying x4 + 44x2 + -576 = 0 Reorder the terms: -576 + 44x2 + x4 = 0 Solving -576 + 44x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '576' to each side of the equation. -576 + 44x2 + 576 + x4 = 0 + 576 Reorder the terms: -576 + 576 + 44x2 + x4 = 0 + 576 Combine like terms: -576 + 576 = 0 0 + 44x2 + x4 = 0 + 576 44x2 + x4 = 0 + 576 Combine like terms: 0 + 576 = 576 44x2 + x4 = 576 The x term is 44x2. Take half its coefficient (22). Square it (484) and add it to both sides. Add '484' to each side of the equation. 44x2 + 484 + x4 = 576 + 484 Reorder the terms: 484 + 44x2 + x4 = 576 + 484 Combine like terms: 576 + 484 = 1060 484 + 44x2 + x4 = 1060 Factor a perfect square on the left side: (x2 + 22)(x2 + 22) = 1060 Calculate the square root of the right side: 32.557641192 Break this problem into two subproblems by setting (x2 + 22) equal to 32.557641192 and -32.557641192.Subproblem 1
x2 + 22 = 32.557641192 Simplifying x2 + 22 = 32.557641192 Reorder the terms: 22 + x2 = 32.557641192 Solving 22 + x2 = 32.557641192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x2 = 32.557641192 + -22 Combine like terms: 22 + -22 = 0 0 + x2 = 32.557641192 + -22 x2 = 32.557641192 + -22 Combine like terms: 32.557641192 + -22 = 10.557641192 x2 = 10.557641192 Simplifying x2 = 10.557641192 Take the square root of each side: x = {-3.249252405, 3.249252405}Subproblem 2
x2 + 22 = -32.557641192 Simplifying x2 + 22 = -32.557641192 Reorder the terms: 22 + x2 = -32.557641192 Solving 22 + x2 = -32.557641192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + x2 = -32.557641192 + -22 Combine like terms: 22 + -22 = 0 0 + x2 = -32.557641192 + -22 x2 = -32.557641192 + -22 Combine like terms: -32.557641192 + -22 = -54.557641192 x2 = -54.557641192 Simplifying x2 = -54.557641192 Reorder the terms: 54.557641192 + x2 = -54.557641192 + 54.557641192 Combine like terms: -54.557641192 + 54.557641192 = 0.000000000 54.557641192 + 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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