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Simplifying 3x4 + -12x2 + 12 = 0 Reorder the terms: 12 + -12x2 + 3x4 = 0 Solving 12 + -12x2 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -4x2 + x4) = 0 Factor a trinomial. 3((2 + -1x2)(2 + -1x2)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -1x2 = 0 Solving 2 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x2 = 0 + -2 -1x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1x2 = -2 Divide each side by '-1'. x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}Subproblem 2
Set the factor '(2 + -1x2)' equal to zero and attempt to solve: Simplifying 2 + -1x2 = 0 Solving 2 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x2 = 0 + -2 -1x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1x2 = -2 Divide each side by '-1'. x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}Solution
x = {-1.414213562, 1.414213562, -1.414213562, 1.414213562}
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