1024=(x-8)(x-8)(4)

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Solution for 1024=(x-8)(x-8)(4) equation:


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 = 24

Subproblem 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 = -8

Solution

x = {24, -8}

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