25x-175=x^2-2x+1

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Solution for 25x-175=x^2-2x+1 equation:


Simplifying
25x + -175 = x2 + -2x + 1

Reorder the terms:
-175 + 25x = x2 + -2x + 1

Reorder the terms:
-175 + 25x = 1 + -2x + x2

Solving
-175 + 25x = 1 + -2x + x2

Solving for variable 'x'.

Reorder the terms:
-175 + -1 + 25x + 2x + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Combine like terms: -175 + -1 = -176
-176 + 25x + 2x + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Combine like terms: 25x + 2x = 27x
-176 + 27x + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2

Reorder the terms:
-176 + 27x + -1x2 = 1 + -1 + -2x + 2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
-176 + 27x + -1x2 = 0 + -2x + 2x + x2 + -1x2
-176 + 27x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
-176 + 27x + -1x2 = 0 + x2 + -1x2
-176 + 27x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-176 + 27x + -1x2 = 0

Factor a trinomial.
(-16 + x)(11 + -1x) = 0

Subproblem 1

Set the factor '(-16 + x)' equal to zero and attempt to solve: Simplifying -16 + x = 0 Solving -16 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 0 + 16 Combine like terms: -16 + 16 = 0 0 + x = 0 + 16 x = 0 + 16 Combine like terms: 0 + 16 = 16 x = 16 Simplifying x = 16

Subproblem 2

Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11

Solution

x = {16, 11}

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