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Simplifying 53x2 + -20x4 = 18 Solving 53x2 + -20x4 = 18 Solving for variable 'x'. Reorder the terms: -18 + 53x2 + -20x4 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 53x2 + -20x4 = 0 Factor a trinomial. (-9 + 4x2)(2 + -5x2) = 0 Factor a difference between two squares. ((3 + 2x)(-3 + 2x))(2 + -5x2) = 0Subproblem 1
Set the factor '(2 + -5x2)' equal to zero and attempt to solve: Simplifying 2 + -5x2 = 0 Solving 2 + -5x2 = 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 + -5x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x2 = 0 + -2 -5x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -5x2 = -2 Divide each side by '-5'. x2 = 0.4 Simplifying x2 = 0.4 Take the square root of each side: x = {-0.632455532, 0.632455532}Subproblem 2
Set the factor '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 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 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Divide each side by '2'. x = -1.5 Simplifying x = -1.5Subproblem 3
Set the factor '(-3 + 2x)' equal to zero and attempt to solve: Simplifying -3 + 2x = 0 Solving -3 + 2x = 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 + 2x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x = 0 + 3 2x = 0 + 3 Combine like terms: 0 + 3 = 3 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5Solution
x = {-0.632455532, 0.632455532, -1.5, 1.5}
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