x^2-14x+23=0

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Solution for x^2-14x+23=0 equation: 


Simplifying
x2 + -14x + 23 = 0

Reorder the terms:
23 + -14x + x2 = 0

Solving
23 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + -14x + -23 + x2 = 0 + -23

Reorder the terms:
23 + -23 + -14x + x2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + -14x + x2 = 0 + -23
-14x + x2 = 0 + -23

Combine like terms: 0 + -23 = -23
-14x + x2 = -23

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 = -23 + 49

Reorder the terms:
49 + -14x + x2 = -23 + 49

Combine like terms: -23 + 49 = 26
49 + -14x + x2 = 26

Factor a perfect square on the left side:
(x + -7)(x + -7) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(x + -7) equal to 5.099019514 and -5.099019514.


Subproblem 1
x + -7 = 5.099019514

Simplifying
x + -7 = 5.099019514

Reorder the terms:
-7 + x = 5.099019514

Solving
-7 + x = 5.099019514

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 = 5.099019514 + 7

Combine like terms: -7 + 7 = 0
0 + x = 5.099019514 + 7
x = 5.099019514 + 7

Combine like terms: 5.099019514 + 7 = 12.099019514
x = 12.099019514

Simplifying
x = 12.099019514


Subproblem 2
x + -7 = -5.099019514

Simplifying
x + -7 = -5.099019514

Reorder the terms:
-7 + x = -5.099019514

Solving
-7 + x = -5.099019514

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 = -5.099019514 + 7

Combine like terms: -7 + 7 = 0
0 + x = -5.099019514 + 7
x = -5.099019514 + 7

Combine like terms: -5.099019514 + 7 = 1.900980486
x = 1.900980486

Simplifying
x = 1.900980486


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.099019514, 1.900980486}

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