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Simplifying 2x4 + -8x2 + -3 = 0 Reorder the terms: -3 + -8x2 + 2x4 = 0 Solving -3 + -8x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -4x2 + x4 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -4x2 + 1.5 + x4 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -4x2 + x4 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -4x2 + x4 = 0 + 1.5 -4x2 + x4 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -4x2 + x4 = 1.5 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 = 1.5 + 4 Reorder the terms: 4 + -4x2 + x4 = 1.5 + 4 Combine like terms: 1.5 + 4 = 5.5 4 + -4x2 + x4 = 5.5 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 5.5 Calculate the square root of the right side: 2.34520788 Break this problem into two subproblems by setting (x2 + -2) equal to 2.34520788 and -2.34520788.Subproblem 1
x2 + -2 = 2.34520788 Simplifying x2 + -2 = 2.34520788 Reorder the terms: -2 + x2 = 2.34520788 Solving -2 + x2 = 2.34520788 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 = 2.34520788 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 2.34520788 + 2 x2 = 2.34520788 + 2 Combine like terms: 2.34520788 + 2 = 4.34520788 x2 = 4.34520788 Simplifying x2 = 4.34520788 Take the square root of each side: x = {-2.084516222, 2.084516222}Subproblem 2
x2 + -2 = -2.34520788 Simplifying x2 + -2 = -2.34520788 Reorder the terms: -2 + x2 = -2.34520788 Solving -2 + x2 = -2.34520788 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 = -2.34520788 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -2.34520788 + 2 x2 = -2.34520788 + 2 Combine like terms: -2.34520788 + 2 = -0.34520788 x2 = -0.34520788 Simplifying x2 = -0.34520788 Reorder the terms: 0.34520788 + x2 = -0.34520788 + 0.34520788 Combine like terms: -0.34520788 + 0.34520788 = 0.00000000 0.34520788 + x2 = 0.00000000 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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