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Simplifying x4 + 6x2 = 10x2 Reorder the terms: 6x2 + x4 = 10x2 Solving 6x2 + x4 = 10x2 Solving for variable 'x'. Reorder the terms: 6x2 + -10x2 + x4 = 10x2 + -10x2 Combine like terms: 6x2 + -10x2 = -4x2 -4x2 + x4 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -4x2 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-4 + x2) = 0 Factor a difference between two squares. x2((2 + x)(-2 + 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 '(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 = {0, -2, 2}
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