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Simplifying 4x4 = 41x2 + -100 Reorder the terms: 4x4 = -100 + 41x2 Solving 4x4 = -100 + 41x2 Solving for variable 'x'. Reorder the terms: 100 + -41x2 + 4x4 = -100 + 41x2 + 100 + -41x2 Reorder the terms: 100 + -41x2 + 4x4 = -100 + 100 + 41x2 + -41x2 Combine like terms: -100 + 100 = 0 100 + -41x2 + 4x4 = 0 + 41x2 + -41x2 100 + -41x2 + 4x4 = 41x2 + -41x2 Combine like terms: 41x2 + -41x2 = 0 100 + -41x2 + 4x4 = 0 Factor a trinomial. (4 + -1x2)(25 + -4x2) = 0 Factor a difference between two squares. ((2 + x)(2 + -1x))(25 + -4x2) = 0 Factor a difference between two squares. ((5 + 2x)(5 + -2x))(2 + x)(2 + -1x) = 0Subproblem 1
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 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 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 = -2.5Subproblem 4
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, 2, -2.5, 2.5}
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