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

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


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

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

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

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

Combine like terms: x2 + x2 = 2x2
20 + -12x + 2x2 = x2

Solving
20 + -12x + 2x2 = x2

Solving for variable 'x'.

Combine like terms: 2x2 + -1x2 = 1x2
20 + -12x + 1x2 = x2 + -1x2

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

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

Subproblem 1

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

Subproblem 2

Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 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 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10

Solution

x = {2, 10}

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