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Simplifying 25x4 + -10x2 + 1 = 0 Reorder the terms: 1 + -10x2 + 25x4 = 0 Solving 1 + -10x2 + 25x4 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -5x2)(1 + -5x2) = 0Subproblem 1
Set the factor '(1 + -5x2)' equal to zero and attempt to solve: Simplifying 1 + -5x2 = 0 Solving 1 + -5x2 = 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 + -5x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x2 = 0 + -1 -5x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5x2 = -1 Divide each side by '-5'. x2 = 0.2 Simplifying x2 = 0.2 Take the square root of each side: x = {-0.447213596, 0.447213596}Subproblem 2
Set the factor '(1 + -5x2)' equal to zero and attempt to solve: Simplifying 1 + -5x2 = 0 Solving 1 + -5x2 = 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 + -5x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x2 = 0 + -1 -5x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -5x2 = -1 Divide each side by '-5'. x2 = 0.2 Simplifying x2 = 0.2 Take the square root of each side: x = {-0.447213596, 0.447213596}Solution
x = {-0.447213596, 0.447213596, -0.447213596, 0.447213596}
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