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Simplifying x4 + -18x2 = 18x2 Reorder the terms: -18x2 + x4 = 18x2 Solving -18x2 + x4 = 18x2 Solving for variable 'x'. Reorder the terms: -18x2 + -18x2 + x4 = 18x2 + -18x2 Combine like terms: -18x2 + -18x2 = -36x2 -36x2 + x4 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -36x2 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-36 + x2) = 0 Factor a difference between two squares. x2((6 + x)(-6 + x)) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Subproblem 3
Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6Solution
x = {0, -6, 6}
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