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Simplifying 1024 = (x + -8)(x + -8)(4) Reorder the terms: 1024 = (-8 + x)(x + -8)(4) Reorder the terms: 1024 = (-8 + x)(-8 + x)(4) Reorder the terms for easier multiplication: 1024 = 4(-8 + x)(-8 + x) Multiply (-8 + x) * (-8 + x) 1024 = 4(-8(-8 + x) + x(-8 + x)) 1024 = 4((-8 * -8 + x * -8) + x(-8 + x)) 1024 = 4((64 + -8x) + x(-8 + x)) 1024 = 4(64 + -8x + (-8 * x + x * x)) 1024 = 4(64 + -8x + (-8x + x2)) Combine like terms: -8x + -8x = -16x 1024 = 4(64 + -16x + x2) 1024 = (64 * 4 + -16x * 4 + x2 * 4) 1024 = (256 + -64x + 4x2) Solving 1024 = 256 + -64x + 4x2 Solving for variable 'x'. Combine like terms: 1024 + -256 = 768 768 + 64x + -4x2 = 256 + -64x + 4x2 + -256 + 64x + -4x2 Reorder the terms: 768 + 64x + -4x2 = 256 + -256 + -64x + 64x + 4x2 + -4x2 Combine like terms: 256 + -256 = 0 768 + 64x + -4x2 = 0 + -64x + 64x + 4x2 + -4x2 768 + 64x + -4x2 = -64x + 64x + 4x2 + -4x2 Combine like terms: -64x + 64x = 0 768 + 64x + -4x2 = 0 + 4x2 + -4x2 768 + 64x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 768 + 64x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(192 + 16x + -1x2) = 0 Factor a trinomial. 4((24 + -1x)(8 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(24 + -1x)' equal to zero and attempt to solve: Simplifying 24 + -1x = 0 Solving 24 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-24' to each side of the equation. 24 + -24 + -1x = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -1x = 0 + -24 -1x = 0 + -24 Combine like terms: 0 + -24 = -24 -1x = -24 Divide each side by '-1'. x = 24 Simplifying x = 24Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Solution
x = {24, -8}
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