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Simplifying 625x4 + -200x2 + 15 = 0 Reorder the terms: 15 + -200x2 + 625x4 = 0 Solving 15 + -200x2 + 625x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -40x2 + 125x4) = 0 Factor a trinomial. 5((3 + -25x2)(1 + -5x2)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -25x2)' equal to zero and attempt to solve: Simplifying 3 + -25x2 = 0 Solving 3 + -25x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -25x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -25x2 = 0 + -3 -25x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -25x2 = -3 Divide each side by '-25'. x2 = 0.12 Simplifying x2 = 0.12 Take the square root of each side: x = {-0.346410162, 0.346410162}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 = {-0.346410162, 0.346410162, -0.447213596, 0.447213596}
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