x^2-14x-10=0

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Solution for x^2-14x-10=0 equation: 


Simplifying
x2 + -14x + -10 = 0

Reorder the terms:
-10 + -14x + x2 = 0

Solving
-10 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -14x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -14x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -14x + x2 = 0 + 10
-14x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-14x + x2 = 10

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 = 10 + 49

Reorder the terms:
49 + -14x + x2 = 10 + 49

Combine like terms: 10 + 49 = 59
49 + -14x + x2 = 59

Factor a perfect square on the left side:
(x + -7)(x + -7) = 59

Calculate the square root of the right side: 7.681145748

Break this problem into two subproblems by setting 
(x + -7) equal to 7.681145748 and -7.681145748.


Subproblem 1
x + -7 = 7.681145748

Simplifying
x + -7 = 7.681145748

Reorder the terms:
-7 + x = 7.681145748

Solving
-7 + x = 7.681145748

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 = 7.681145748 + 7

Combine like terms: -7 + 7 = 0
0 + x = 7.681145748 + 7
x = 7.681145748 + 7

Combine like terms: 7.681145748 + 7 = 14.681145748
x = 14.681145748

Simplifying
x = 14.681145748


Subproblem 2
x + -7 = -7.681145748

Simplifying
x + -7 = -7.681145748

Reorder the terms:
-7 + x = -7.681145748

Solving
-7 + x = -7.681145748

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 = -7.681145748 + 7

Combine like terms: -7 + 7 = 0
0 + x = -7.681145748 + 7
x = -7.681145748 + 7

Combine like terms: -7.681145748 + 7 = -0.681145748
x = -0.681145748

Simplifying
x = -0.681145748


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.681145748, -0.681145748}

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