X^2-14X+7=0

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Solution for X^2-14X+7=0 equation: 


Simplifying
X2 + -14X + 7 = 0

Reorder the terms:
7 + -14X + X2 = 0

Solving
7 + -14X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -14X + -7 + X2 = 0 + -7

Reorder the terms:
7 + -7 + -14X + X2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -14X + X2 = 0 + -7
-14X + X2 = 0 + -7

Combine like terms: 0 + -7 = -7
-14X + X2 = -7

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 = -7 + 49

Reorder the terms:
49 + -14X + X2 = -7 + 49

Combine like terms: -7 + 49 = 42
49 + -14X + X2 = 42

Factor a perfect square on the left side:
(X + -7)(X + -7) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(X + -7) equal to 6.480740698 and -6.480740698.


Subproblem 1
X + -7 = 6.480740698

Simplifying
X + -7 = 6.480740698

Reorder the terms:
-7 + X = 6.480740698

Solving
-7 + X = 6.480740698

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 = 6.480740698 + 7

Combine like terms: -7 + 7 = 0
0 + X = 6.480740698 + 7
X = 6.480740698 + 7

Combine like terms: 6.480740698 + 7 = 13.480740698
X = 13.480740698

Simplifying
X = 13.480740698


Subproblem 2
X + -7 = -6.480740698

Simplifying
X + -7 = -6.480740698

Reorder the terms:
-7 + X = -6.480740698

Solving
-7 + X = -6.480740698

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 = -6.480740698 + 7

Combine like terms: -7 + 7 = 0
0 + X = -6.480740698 + 7
X = -6.480740698 + 7

Combine like terms: -6.480740698 + 7 = 0.519259302
X = 0.519259302

Simplifying
X = 0.519259302


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {13.480740698, 0.519259302}

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