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Simplifying 0.25x4 + -1x2 + -4 = 0 Reorder the terms: -4 + -1x2 + 0.25x4 = 0 Solving -4 + -1x2 + 0.25x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -16 + -4x2 + x4 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -4x2 + 16 + x4 = 0 + 16 Reorder the terms: -16 + 16 + -4x2 + x4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -4x2 + x4 = 0 + 16 -4x2 + x4 = 0 + 16 Combine like terms: 0 + 16 = 16 -4x2 + x4 = 16 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 = 16 + 4 Reorder the terms: 4 + -4x2 + x4 = 16 + 4 Combine like terms: 16 + 4 = 20 4 + -4x2 + x4 = 20 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x2 + -2) equal to 4.472135955 and -4.472135955.Subproblem 1
x2 + -2 = 4.472135955 Simplifying x2 + -2 = 4.472135955 Reorder the terms: -2 + x2 = 4.472135955 Solving -2 + x2 = 4.472135955 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 = 4.472135955 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 4.472135955 + 2 x2 = 4.472135955 + 2 Combine like terms: 4.472135955 + 2 = 6.472135955 x2 = 6.472135955 Simplifying x2 = 6.472135955 Take the square root of each side: x = {-2.544039299, 2.544039299}Subproblem 2
x2 + -2 = -4.472135955 Simplifying x2 + -2 = -4.472135955 Reorder the terms: -2 + x2 = -4.472135955 Solving -2 + x2 = -4.472135955 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 = -4.472135955 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -4.472135955 + 2 x2 = -4.472135955 + 2 Combine like terms: -4.472135955 + 2 = -2.472135955 x2 = -2.472135955 Simplifying x2 = -2.472135955 Reorder the terms: 2.472135955 + x2 = -2.472135955 + 2.472135955 Combine like terms: -2.472135955 + 2.472135955 = 0.000000000 2.472135955 + 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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