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Simplifying -18x4 + -48x2 + -96 = 0 Reorder the terms: -96 + -48x2 + -18x4 = 0 Solving -96 + -48x2 + -18x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-6'. -6(16 + 8x2 + 3x4) = 0 Ignore the factor -6.Subproblem 1
Set the factor '(16 + 8x2 + 3x4)' equal to zero and attempt to solve: Simplifying 16 + 8x2 + 3x4 = 0 Solving 16 + 8x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5.333333333 + 2.666666667x2 + x4 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + 2.666666667x2 + -5.333333333 + x4 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + 2.666666667x2 + x4 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + 2.666666667x2 + x4 = 0 + -5.333333333 2.666666667x2 + x4 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 2.666666667x2 + x4 = -5.333333333 The x term is 2.666666667x2. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667x2 + 1.777777780 + x4 = -5.333333333 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667x2 + x4 = -5.333333333 + 1.777777780 Combine like terms: -5.333333333 + 1.777777780 = -3.555555553 1.777777780 + 2.666666667x2 + x4 = -3.555555553 Factor a perfect square on the left side: (x2 + 1.333333334)(x2 + 1.333333334) = -3.555555553 Can't calculate square root of the right side. 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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