X^2-14X-9=0

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Solution for X^2-14X-9=0 equation: 


Simplifying
X2 + -14X + -9 = 0

Reorder the terms:
-9 + -14X + X2 = 0

Solving
-9 + -14X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -14X + 9 + X2 = 0 + 9

Reorder the terms:
-9 + 9 + -14X + X2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -14X + X2 = 0 + 9
-14X + X2 = 0 + 9

Combine like terms: 0 + 9 = 9
-14X + X2 = 9

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 = 9 + 49

Reorder the terms:
49 + -14X + X2 = 9 + 49

Combine like terms: 9 + 49 = 58
49 + -14X + X2 = 58

Factor a perfect square on the left side:
(X + -7)(X + -7) = 58

Calculate the square root of the right side: 7.615773106

Break this problem into two subproblems by setting 
(X + -7) equal to 7.615773106 and -7.615773106.


Subproblem 1
X + -7 = 7.615773106

Simplifying
X + -7 = 7.615773106

Reorder the terms:
-7 + X = 7.615773106

Solving
-7 + X = 7.615773106

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 = 7.615773106 + 7

Combine like terms: -7 + 7 = 0
0 + X = 7.615773106 + 7
X = 7.615773106 + 7

Combine like terms: 7.615773106 + 7 = 14.615773106
X = 14.615773106

Simplifying
X = 14.615773106


Subproblem 2
X + -7 = -7.615773106

Simplifying
X + -7 = -7.615773106

Reorder the terms:
-7 + X = -7.615773106

Solving
-7 + X = -7.615773106

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 = -7.615773106 + 7

Combine like terms: -7 + 7 = 0
0 + X = -7.615773106 + 7
X = -7.615773106 + 7

Combine like terms: -7.615773106 + 7 = -0.615773106
X = -0.615773106

Simplifying
X = -0.615773106


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {14.615773106, -0.615773106}

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