x^2-14x+17=0

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Solution for x^2-14x+17=0 equation: 


Simplifying
x2 + -14x + 17 = 0

Reorder the terms:
17 + -14x + x2 = 0

Solving
17 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -14x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + -14x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -14x + x2 = 0 + -17
-14x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
-14x + x2 = -17

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 = -17 + 49

Reorder the terms:
49 + -14x + x2 = -17 + 49

Combine like terms: -17 + 49 = 32
49 + -14x + x2 = 32

Factor a perfect square on the left side:
(x + -7)(x + -7) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(x + -7) equal to 5.656854249 and -5.656854249.


Subproblem 1
x + -7 = 5.656854249

Simplifying
x + -7 = 5.656854249

Reorder the terms:
-7 + x = 5.656854249

Solving
-7 + x = 5.656854249

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 = 5.656854249 + 7

Combine like terms: -7 + 7 = 0
0 + x = 5.656854249 + 7
x = 5.656854249 + 7

Combine like terms: 5.656854249 + 7 = 12.656854249
x = 12.656854249

Simplifying
x = 12.656854249


Subproblem 2
x + -7 = -5.656854249

Simplifying
x + -7 = -5.656854249

Reorder the terms:
-7 + x = -5.656854249

Solving
-7 + x = -5.656854249

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 = -5.656854249 + 7

Combine like terms: -7 + 7 = 0
0 + x = -5.656854249 + 7
x = -5.656854249 + 7

Combine like terms: -5.656854249 + 7 = 1.343145751
x = 1.343145751

Simplifying
x = 1.343145751


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.656854249, 1.343145751}

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