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Simplifying 0 = (3x4 + 128x2 + 256) Reorder the terms: 0 = (256 + 128x2 + 3x4) Remove parenthesis around (256 + 128x2 + 3x4) 0 = 256 + 128x2 + 3x4 Solving 0 = 256 + 128x2 + 3x4 Solving for variable 'x'. Combine like terms: 0 + -256 = -256 -256 + -128x2 + -3x4 = 256 + 128x2 + 3x4 + -256 + -128x2 + -3x4 Reorder the terms: -256 + -128x2 + -3x4 = 256 + -256 + 128x2 + -128x2 + 3x4 + -3x4 Combine like terms: 256 + -256 = 0 -256 + -128x2 + -3x4 = 0 + 128x2 + -128x2 + 3x4 + -3x4 -256 + -128x2 + -3x4 = 128x2 + -128x2 + 3x4 + -3x4 Combine like terms: 128x2 + -128x2 = 0 -256 + -128x2 + -3x4 = 0 + 3x4 + -3x4 -256 + -128x2 + -3x4 = 3x4 + -3x4 Combine like terms: 3x4 + -3x4 = 0 -256 + -128x2 + -3x4 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(256 + 128x2 + 3x4) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(256 + 128x2 + 3x4)' equal to zero and attempt to solve: Simplifying 256 + 128x2 + 3x4 = 0 Solving 256 + 128x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 85.33333333 + 42.66666667x2 + x4 = 0 Move the constant term to the right: Add '-85.33333333' to each side of the equation. 85.33333333 + 42.66666667x2 + -85.33333333 + x4 = 0 + -85.33333333 Reorder the terms: 85.33333333 + -85.33333333 + 42.66666667x2 + x4 = 0 + -85.33333333 Combine like terms: 85.33333333 + -85.33333333 = 0.00000000 0.00000000 + 42.66666667x2 + x4 = 0 + -85.33333333 42.66666667x2 + x4 = 0 + -85.33333333 Combine like terms: 0 + -85.33333333 = -85.33333333 42.66666667x2 + x4 = -85.33333333 The x term is 42.66666667x2. Take half its coefficient (21.33333334). Square it (455.1111114) and add it to both sides. Add '455.1111114' to each side of the equation. 42.66666667x2 + 455.1111114 + x4 = -85.33333333 + 455.1111114 Reorder the terms: 455.1111114 + 42.66666667x2 + x4 = -85.33333333 + 455.1111114 Combine like terms: -85.33333333 + 455.1111114 = 369.77777807 455.1111114 + 42.66666667x2 + x4 = 369.77777807 Factor a perfect square on the left side: (x2 + 21.33333334)(x2 + 21.33333334) = 369.77777807 Calculate the square root of the right side: 19.22960681 Break this problem into two subproblems by setting (x2 + 21.33333334) equal to 19.22960681 and -19.22960681.Subproblem 1
x2 + 21.33333334 = 19.22960681 Simplifying x2 + 21.33333334 = 19.22960681 Reorder the terms: 21.33333334 + x2 = 19.22960681 Solving 21.33333334 + x2 = 19.22960681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.33333334' to each side of the equation. 21.33333334 + -21.33333334 + x2 = 19.22960681 + -21.33333334 Combine like terms: 21.33333334 + -21.33333334 = 0.00000000 0.00000000 + x2 = 19.22960681 + -21.33333334 x2 = 19.22960681 + -21.33333334 Combine like terms: 19.22960681 + -21.33333334 = -2.10372653 x2 = -2.10372653 Simplifying x2 = -2.10372653 Reorder the terms: 2.10372653 + x2 = -2.10372653 + 2.10372653 Combine like terms: -2.10372653 + 2.10372653 = 0.00000000 2.10372653 + x2 = 0.00000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 21.33333334 = -19.22960681 Simplifying x2 + 21.33333334 = -19.22960681 Reorder the terms: 21.33333334 + x2 = -19.22960681 Solving 21.33333334 + x2 = -19.22960681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.33333334' to each side of the equation. 21.33333334 + -21.33333334 + x2 = -19.22960681 + -21.33333334 Combine like terms: 21.33333334 + -21.33333334 = 0.00000000 0.00000000 + x2 = -19.22960681 + -21.33333334 x2 = -19.22960681 + -21.33333334 Combine like terms: -19.22960681 + -21.33333334 = -40.56294015 x2 = -40.56294015 Simplifying x2 = -40.56294015 Reorder the terms: 40.56294015 + x2 = -40.56294015 + 40.56294015 Combine like terms: -40.56294015 + 40.56294015 = 0.00000000 40.56294015 + 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. 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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