4x-4=x^2-8x+16

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Solution for 4x-4=x^2-8x+16 equation:


Simplifying
4x + -4 = x2 + -8x + 16

Reorder the terms:
-4 + 4x = x2 + -8x + 16

Reorder the terms:
-4 + 4x = 16 + -8x + x2

Solving
-4 + 4x = 16 + -8x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + -16 + 4x + 8x + -1x2 = 16 + -8x + x2 + -16 + 8x + -1x2

Combine like terms: -4 + -16 = -20
-20 + 4x + 8x + -1x2 = 16 + -8x + x2 + -16 + 8x + -1x2

Combine like terms: 4x + 8x = 12x
-20 + 12x + -1x2 = 16 + -8x + x2 + -16 + 8x + -1x2

Reorder the terms:
-20 + 12x + -1x2 = 16 + -16 + -8x + 8x + x2 + -1x2

Combine like terms: 16 + -16 = 0
-20 + 12x + -1x2 = 0 + -8x + 8x + x2 + -1x2
-20 + 12x + -1x2 = -8x + 8x + x2 + -1x2

Combine like terms: -8x + 8x = 0
-20 + 12x + -1x2 = 0 + x2 + -1x2
-20 + 12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-20 + 12x + -1x2 = 0

Factor a trinomial.
(-10 + x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-10 + x)' equal to zero and attempt to solve: Simplifying -10 + x = 0 Solving -10 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + x = 0 + 10 x = 0 + 10 Combine like terms: 0 + 10 = 10 x = 10 Simplifying x = 10

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {10, 2}

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