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Simplifying -8x4 + -12x2 + 1 = 0 Reorder the terms: 1 + -12x2 + -8x4 = 0 Solving 1 + -12x2 + -8x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.125 + 1.5x2 + x4 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + 1.5x2 + 0.125 + x4 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + 1.5x2 + x4 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + 1.5x2 + x4 = 0 + 0.125 1.5x2 + x4 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 1.5x2 + x4 = 0.125 The x term is 1.5x2. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x2 + 0.5625 + x4 = 0.125 + 0.5625 Reorder the terms: 0.5625 + 1.5x2 + x4 = 0.125 + 0.5625 Combine like terms: 0.125 + 0.5625 = 0.6875 0.5625 + 1.5x2 + x4 = 0.6875 Factor a perfect square on the left side: (x2 + 0.75)(x2 + 0.75) = 0.6875 Calculate the square root of the right side: 0.829156198 Break this problem into two subproblems by setting (x2 + 0.75) equal to 0.829156198 and -0.829156198.Subproblem 1
x2 + 0.75 = 0.829156198 Simplifying x2 + 0.75 = 0.829156198 Reorder the terms: 0.75 + x2 = 0.829156198 Solving 0.75 + x2 = 0.829156198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x2 = 0.829156198 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x2 = 0.829156198 + -0.75 x2 = 0.829156198 + -0.75 Combine like terms: 0.829156198 + -0.75 = 0.079156198 x2 = 0.079156198 Simplifying x2 = 0.079156198 Take the square root of each side: x = {-0.281347113, 0.281347113}Subproblem 2
x2 + 0.75 = -0.829156198 Simplifying x2 + 0.75 = -0.829156198 Reorder the terms: 0.75 + x2 = -0.829156198 Solving 0.75 + x2 = -0.829156198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x2 = -0.829156198 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x2 = -0.829156198 + -0.75 x2 = -0.829156198 + -0.75 Combine like terms: -0.829156198 + -0.75 = -1.579156198 x2 = -1.579156198 Simplifying x2 = -1.579156198 Reorder the terms: 1.579156198 + x2 = -1.579156198 + 1.579156198 Combine like terms: -1.579156198 + 1.579156198 = 0.000000000 1.579156198 + 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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