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Simplifying 2x4 + -40x2 + 72 = 0 Reorder the terms: 72 + -40x2 + 2x4 = 0 Solving 72 + -40x2 + 2x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(36 + -20x2 + x4) = 0 Factor a trinomial. 2((2 + -1x2)(18 + -1x2)) = 0 Ignore the factor 2.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 '(18 + -1x2)' equal to zero and attempt to solve: Simplifying 18 + -1x2 = 0 Solving 18 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1x2 = 0 + -18 -1x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -1x2 = -18 Divide each side by '-1'. x2 = 18 Simplifying x2 = 18 Take the square root of each side: x = {-4.242640687, 4.242640687}Solution
x = {-1.414213562, 1.414213562, -4.242640687, 4.242640687}
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