2x^2-14x+49=x^2+2x+1

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Solution for 2x^2-14x+49=x^2+2x+1 equation: 


Simplifying
2x2 + -14x + 49 = x2 + 2x + 1

Reorder the terms:
49 + -14x + 2x2 = x2 + 2x + 1

Reorder the terms:
49 + -14x + 2x2 = 1 + 2x + x2

Solving
49 + -14x + 2x2 = 1 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
49 + -1 + -14x + -2x + 2x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: 49 + -1 = 48
48 + -14x + -2x + 2x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: -14x + -2x = -16x
48 + -16x + 2x2 + -1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
48 + -16x + 1x2 = 1 + 2x + x2 + -1 + -2x + -1x2

Reorder the terms:
48 + -16x + 1x2 = 1 + -1 + 2x + -2x + x2 + -1x2

Combine like terms: 1 + -1 = 0
48 + -16x + 1x2 = 0 + 2x + -2x + x2 + -1x2
48 + -16x + 1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
48 + -16x + 1x2 = 0 + x2 + -1x2
48 + -16x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
48 + -16x + 1x2 = 0

Factor a trinomial.
(4 + -1x)(12 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

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

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

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {4, 12}

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