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Simplifying 8x2 + x4 + -400 = 0 Reorder the terms: -400 + 8x2 + x4 = 0 Solving -400 + 8x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 8x2 + 400 + x4 = 0 + 400 Reorder the terms: -400 + 400 + 8x2 + x4 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 8x2 + x4 = 0 + 400 8x2 + x4 = 0 + 400 Combine like terms: 0 + 400 = 400 8x2 + x4 = 400 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 = 400 + 16 Reorder the terms: 16 + 8x2 + x4 = 400 + 16 Combine like terms: 400 + 16 = 416 16 + 8x2 + x4 = 416 Factor a perfect square on the left side: (x2 + 4)(x2 + 4) = 416 Calculate the square root of the right side: 20.396078054 Break this problem into two subproblems by setting (x2 + 4) equal to 20.396078054 and -20.396078054.Subproblem 1
x2 + 4 = 20.396078054 Simplifying x2 + 4 = 20.396078054 Reorder the terms: 4 + x2 = 20.396078054 Solving 4 + x2 = 20.396078054 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 = 20.396078054 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 20.396078054 + -4 x2 = 20.396078054 + -4 Combine like terms: 20.396078054 + -4 = 16.396078054 x2 = 16.396078054 Simplifying x2 = 16.396078054 Take the square root of each side: x = {-4.04920709, 4.04920709}Subproblem 2
x2 + 4 = -20.396078054 Simplifying x2 + 4 = -20.396078054 Reorder the terms: 4 + x2 = -20.396078054 Solving 4 + x2 = -20.396078054 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 = -20.396078054 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = -20.396078054 + -4 x2 = -20.396078054 + -4 Combine like terms: -20.396078054 + -4 = -24.396078054 x2 = -24.396078054 Simplifying x2 = -24.396078054 Reorder the terms: 24.396078054 + x2 = -24.396078054 + 24.396078054 Combine like terms: -24.396078054 + 24.396078054 = 0.000000000 24.396078054 + 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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