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Simplifying 6x4 + 12x2 + 14 = 0 Reorder the terms: 14 + 12x2 + 6x4 = 0 Solving 14 + 12x2 + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 6x2 + 3x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 6x2 + 3x4)' equal to zero and attempt to solve: Simplifying 7 + 6x2 + 3x4 = 0 Solving 7 + 6x2 + 3x4 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.333333333 + 2x2 + x4 = 0 Move the constant term to the right: Add '-2.333333333' to each side of the equation. 2.333333333 + 2x2 + -2.333333333 + x4 = 0 + -2.333333333 Reorder the terms: 2.333333333 + -2.333333333 + 2x2 + x4 = 0 + -2.333333333 Combine like terms: 2.333333333 + -2.333333333 = 0.000000000 0.000000000 + 2x2 + x4 = 0 + -2.333333333 2x2 + x4 = 0 + -2.333333333 Combine like terms: 0 + -2.333333333 = -2.333333333 2x2 + x4 = -2.333333333 The x term is 2x2. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x2 + 1 + x4 = -2.333333333 + 1 Reorder the terms: 1 + 2x2 + x4 = -2.333333333 + 1 Combine like terms: -2.333333333 + 1 = -1.333333333 1 + 2x2 + x4 = -1.333333333 Factor a perfect square on the left side: (x2 + 1)(x2 + 1) = -1.333333333 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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