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Simplifying 5x4 + -18x2 + 16 = 0 Reorder the terms: 16 + -18x2 + 5x4 = 0 Solving 16 + -18x2 + 5x4 = 0 Solving for variable 'x'. Factor a trinomial. (8 + -5x2)(2 + -1x2) = 0Subproblem 1
Set the factor '(8 + -5x2)' equal to zero and attempt to solve: Simplifying 8 + -5x2 = 0 Solving 8 + -5x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -5x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x2 = 0 + -8 -5x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -5x2 = -8 Divide each side by '-5'. x2 = 1.6 Simplifying x2 = 1.6 Take the square root of each side: x = {-1.264911064, 1.264911064}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 = {-1.264911064, 1.264911064, -1.414213562, 1.414213562}
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