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Simplifying -4x4 + 21x2 + -20 = 0 Reorder the terms: -20 + 21x2 + -4x4 = 0 Solving -20 + 21x2 + -4x4 = 0 Solving for variable 'x'. Factor a trinomial. (-4 + x2)(5 + -4x2) = 0 Factor a difference between two squares. ((2 + x)(-2 + x))(5 + -4x2) = 0Subproblem 1
Set the factor '(5 + -4x2)' equal to zero and attempt to solve: Simplifying 5 + -4x2 = 0 Solving 5 + -4x2 = 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 + -4x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x2 = 0 + -5 -4x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -4x2 = -5 Divide each side by '-4'. x2 = 1.25 Simplifying x2 = 1.25 Take the square root of each side: x = {-1.118033989, 1.118033989}Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 3
Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Solution
x = {-1.118033989, 1.118033989, -2, 2}
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