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Simplifying 0.25x4 + 3x2 + -4 = 0 Reorder the terms: -4 + 3x2 + 0.25x4 = 0 Solving -4 + 3x2 + 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 + 12x2 + x4 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 12x2 + 16 + x4 = 0 + 16 Reorder the terms: -16 + 16 + 12x2 + x4 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 12x2 + x4 = 0 + 16 12x2 + x4 = 0 + 16 Combine like terms: 0 + 16 = 16 12x2 + x4 = 16 The x term is 12x2. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x2 + 36 + x4 = 16 + 36 Reorder the terms: 36 + 12x2 + x4 = 16 + 36 Combine like terms: 16 + 36 = 52 36 + 12x2 + x4 = 52 Factor a perfect square on the left side: (x2 + 6)(x2 + 6) = 52 Calculate the square root of the right side: 7.211102551 Break this problem into two subproblems by setting (x2 + 6) equal to 7.211102551 and -7.211102551.Subproblem 1
x2 + 6 = 7.211102551 Simplifying x2 + 6 = 7.211102551 Reorder the terms: 6 + x2 = 7.211102551 Solving 6 + x2 = 7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x2 = 7.211102551 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = 7.211102551 + -6 x2 = 7.211102551 + -6 Combine like terms: 7.211102551 + -6 = 1.211102551 x2 = 1.211102551 Simplifying x2 = 1.211102551 Take the square root of each side: x = {-1.100501045, 1.100501045}Subproblem 2
x2 + 6 = -7.211102551 Simplifying x2 + 6 = -7.211102551 Reorder the terms: 6 + x2 = -7.211102551 Solving 6 + x2 = -7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x2 = -7.211102551 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = -7.211102551 + -6 x2 = -7.211102551 + -6 Combine like terms: -7.211102551 + -6 = -13.211102551 x2 = -13.211102551 Simplifying x2 = -13.211102551 Reorder the terms: 13.211102551 + x2 = -13.211102551 + 13.211102551 Combine like terms: -13.211102551 + 13.211102551 = 0.000000000 13.211102551 + 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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