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Simplifying -4X5 = 44X + -48X3 Solving -4X5 = 44X + -48X3 Solving for variable 'X'. Reorder the terms: -44X + 48X3 + -4X5 = 44X + -48X3 + -44X + 48X3 Reorder the terms: -44X + 48X3 + -4X5 = 44X + -44X + -48X3 + 48X3 Combine like terms: 44X + -44X = 0 -44X + 48X3 + -4X5 = 0 + -48X3 + 48X3 -44X + 48X3 + -4X5 = -48X3 + 48X3 Combine like terms: -48X3 + 48X3 = 0 -44X + 48X3 + -4X5 = 0 Factor out the Greatest Common Factor (GCF), '4X'. 4X(-11 + 12X2 + -1X4) = 0 Factor a trinomial. 4X((-11 + X2)(1 + -1X2)) = 0 Factor a difference between two squares. 4X((-11 + X2)((1 + X)(1 + -1X))) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'X' equal to zero and attempt to solve: Simplifying X = 0 Solving X = 0 Move all terms containing X to the left, all other terms to the right. Simplifying X = 0Subproblem 2
Set the factor '(-11 + X2)' equal to zero and attempt to solve: Simplifying -11 + X2 = 0 Solving -11 + X2 = 0 Move all terms containing X to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + X2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + X2 = 0 + 11 X2 = 0 + 11 Combine like terms: 0 + 11 = 11 X2 = 11 Simplifying X2 = 11 Take the square root of each side: X = {-3.31662479, 3.31662479}Subproblem 3
Set the factor '(1 + X)' equal to zero and attempt to solve: Simplifying 1 + X = 0 Solving 1 + X = 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 + X = 0 + -1 Combine like terms: 1 + -1 = 0 0 + X = 0 + -1 X = 0 + -1 Combine like terms: 0 + -1 = -1 X = -1 Simplifying X = -1Subproblem 4
Set the factor '(1 + -1X)' equal to zero and attempt to solve: Simplifying 1 + -1X = 0 Solving 1 + -1X = 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 + -1X = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1X = 0 + -1 -1X = 0 + -1 Combine like terms: 0 + -1 = -1 -1X = -1 Divide each side by '-1'. X = 1 Simplifying X = 1Solution
X = {0, -3.31662479, 3.31662479, -1, 1}
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