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Simplifying (x2 + 4)(x2 + 4) + 32 = 12x2 + 48 Reorder the terms: (4 + x2)(x2 + 4) + 32 = 12x2 + 48 Reorder the terms: (4 + x2)(4 + x2) + 32 = 12x2 + 48 Multiply (4 + x2) * (4 + x2) (4(4 + x2) + x2(4 + x2)) + 32 = 12x2 + 48 ((4 * 4 + x2 * 4) + x2(4 + x2)) + 32 = 12x2 + 48 ((16 + 4x2) + x2(4 + x2)) + 32 = 12x2 + 48 (16 + 4x2 + (4 * x2 + x2 * x2)) + 32 = 12x2 + 48 (16 + 4x2 + (4x2 + x4)) + 32 = 12x2 + 48 Combine like terms: 4x2 + 4x2 = 8x2 (16 + 8x2 + x4) + 32 = 12x2 + 48 Reorder the terms: 16 + 32 + 8x2 + x4 = 12x2 + 48 Combine like terms: 16 + 32 = 48 48 + 8x2 + x4 = 12x2 + 48 Reorder the terms: 48 + 8x2 + x4 = 48 + 12x2 Add '-48' to each side of the equation. 48 + 8x2 + -48 + x4 = 48 + -48 + 12x2 Reorder the terms: 48 + -48 + 8x2 + x4 = 48 + -48 + 12x2 Combine like terms: 48 + -48 = 0 0 + 8x2 + x4 = 48 + -48 + 12x2 8x2 + x4 = 48 + -48 + 12x2 Combine like terms: 48 + -48 = 0 8x2 + x4 = 0 + 12x2 8x2 + x4 = 12x2 Solving 8x2 + x4 = 12x2 Solving for variable 'x'. Reorder the terms: 8x2 + -12x2 + x4 = 12x2 + -12x2 Combine like terms: 8x2 + -12x2 = -4x2 -4x2 + x4 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 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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