x^2+5=5x

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Solution for x^2+5=5x equation: 


Simplifying
x2 + 5 = 5x

Reorder the terms:
5 + x2 = 5x

Solving
5 + x2 = 5x

Solving for variable 'x'.

Reorder the terms:
5 + -5x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
5 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -5x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -5x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -5x + x2 = 0 + -5
-5x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-5x + x2 = -5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -5 + 6.25

Combine like terms: -5 + 6.25 = 1.25
6.25 + -5x + x2 = 1.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
x + -2.5 = 1.118033989

Simplifying
x + -2.5 = 1.118033989

Reorder the terms:
-2.5 + x = 1.118033989

Solving
-2.5 + x = 1.118033989

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 1.118033989 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.118033989 + 2.5
x = 1.118033989 + 2.5

Combine like terms: 1.118033989 + 2.5 = 3.618033989
x = 3.618033989

Simplifying
x = 3.618033989


Subproblem 2
x + -2.5 = -1.118033989

Simplifying
x + -2.5 = -1.118033989

Reorder the terms:
-2.5 + x = -1.118033989

Solving
-2.5 + x = -1.118033989

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -1.118033989 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.118033989 + 2.5
x = -1.118033989 + 2.5

Combine like terms: -1.118033989 + 2.5 = 1.381966011
x = 1.381966011

Simplifying
x = 1.381966011


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.618033989, 1.381966011}

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