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Simplifying 8x4 + -17x2 + 2 = 0 Reorder the terms: 2 + -17x2 + 8x4 = 0 Solving 2 + -17x2 + 8x4 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -8x2)(2 + -1x2) = 0Subproblem 1
Set the factor '(1 + -8x2)' equal to zero and attempt to solve: Simplifying 1 + -8x2 = 0 Solving 1 + -8x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -8x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8x2 = 0 + -1 -8x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -8x2 = -1 Divide each side by '-8'. x2 = 0.125 Simplifying x2 = 0.125 Take the square root of each side: x = {-0.353553391, 0.353553391}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 = {-0.353553391, 0.353553391, -1.414213562, 1.414213562}
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