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Simplifying 0 = 20x4 + -45x2 + -500 Reorder the terms: 0 = -500 + -45x2 + 20x4 Solving 0 = -500 + -45x2 + 20x4 Solving for variable 'x'. Combine like terms: 0 + 500 = 500 500 + 45x2 + -20x4 = -500 + -45x2 + 20x4 + 500 + 45x2 + -20x4 Reorder the terms: 500 + 45x2 + -20x4 = -500 + 500 + -45x2 + 45x2 + 20x4 + -20x4 Combine like terms: -500 + 500 = 0 500 + 45x2 + -20x4 = 0 + -45x2 + 45x2 + 20x4 + -20x4 500 + 45x2 + -20x4 = -45x2 + 45x2 + 20x4 + -20x4 Combine like terms: -45x2 + 45x2 = 0 500 + 45x2 + -20x4 = 0 + 20x4 + -20x4 500 + 45x2 + -20x4 = 20x4 + -20x4 Combine like terms: 20x4 + -20x4 = 0 500 + 45x2 + -20x4 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(100 + 9x2 + -4x4) = 0 Factor a trinomial. 5((25 + -4x2)(4 + x2)) = 0 Factor a difference between two squares. 5(((5 + 2x)(5 + -2x))(4 + x2)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(4 + x2)' equal to zero and attempt to solve: Simplifying 4 + x2 = 0 Solving 4 + x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x2 = 0 + -4 x2 = 0 + -4 Combine like terms: 0 + -4 = -4 x2 = -4 Simplifying x2 = -4 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5Subproblem 3
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {-2.5, 2.5}
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