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Simplifying 6x4 + -49x2 + 100 = 0 Reorder the terms: 100 + -49x2 + 6x4 = 0 Solving 100 + -49x2 + 6x4 = 0 Solving for variable 'x'. Factor a trinomial. (4 + -1x2)(25 + -6x2) = 0 Factor a difference between two squares. ((2 + x)(2 + -1x))(25 + -6x2) = 0Subproblem 1
Set the factor '(25 + -6x2)' equal to zero and attempt to solve: Simplifying 25 + -6x2 = 0 Solving 25 + -6x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -6x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -6x2 = 0 + -25 -6x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -6x2 = -25 Divide each side by '-6'. x2 = 4.166666667 Simplifying x2 = 4.166666667 Take the square root of each side: x = {-2.041241452, 2.041241452}Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Solution
x = {-2.041241452, 2.041241452, -2, 2}
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