x^2-14x+19=0

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Solution for x^2-14x+19=0 equation: 


Simplifying
x2 + -14x + 19 = 0

Reorder the terms:
19 + -14x + x2 = 0

Solving
19 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + -14x + -19 + x2 = 0 + -19

Reorder the terms:
19 + -19 + -14x + x2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -14x + x2 = 0 + -19
-14x + x2 = 0 + -19

Combine like terms: 0 + -19 = -19
-14x + x2 = -19

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -19 + 49

Reorder the terms:
49 + -14x + x2 = -19 + 49

Combine like terms: -19 + 49 = 30
49 + -14x + x2 = 30

Factor a perfect square on the left side:
(x + -7)(x + -7) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(x + -7) equal to 5.477225575 and -5.477225575.


Subproblem 1
x + -7 = 5.477225575

Simplifying
x + -7 = 5.477225575

Reorder the terms:
-7 + x = 5.477225575

Solving
-7 + x = 5.477225575

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 5.477225575 + 7

Combine like terms: -7 + 7 = 0
0 + x = 5.477225575 + 7
x = 5.477225575 + 7

Combine like terms: 5.477225575 + 7 = 12.477225575
x = 12.477225575

Simplifying
x = 12.477225575


Subproblem 2
x + -7 = -5.477225575

Simplifying
x + -7 = -5.477225575

Reorder the terms:
-7 + x = -5.477225575

Solving
-7 + x = -5.477225575

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -5.477225575 + 7

Combine like terms: -7 + 7 = 0
0 + x = -5.477225575 + 7
x = -5.477225575 + 7

Combine like terms: -5.477225575 + 7 = 1.522774425
x = 1.522774425

Simplifying
x = 1.522774425


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.477225575, 1.522774425}

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