x^2-x+11=7x-5

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Solution for x^2-x+11=7x-5 equation: 


Simplifying
x2 + -1x + 11 = 7x + -5

Reorder the terms:
11 + -1x + x2 = 7x + -5

Reorder the terms:
11 + -1x + x2 = -5 + 7x

Solving
11 + -1x + x2 = -5 + 7x

Solving for variable 'x'.

Reorder the terms:
11 + 5 + -1x + -7x + x2 = -5 + 7x + 5 + -7x

Combine like terms: 11 + 5 = 16
16 + -1x + -7x + x2 = -5 + 7x + 5 + -7x

Combine like terms: -1x + -7x = -8x
16 + -8x + x2 = -5 + 7x + 5 + -7x

Reorder the terms:
16 + -8x + x2 = -5 + 5 + 7x + -7x

Combine like terms: -5 + 5 = 0
16 + -8x + x2 = 0 + 7x + -7x
16 + -8x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
16 + -8x + x2 = 0

Factor a trinomial.
(4 + -1x)(4 + -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 '(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
Solution
x = {4, 4}

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