x^2-14x-63=0

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Solution for x^2-14x-63=0 equation: 


Simplifying
x2 + -14x + -63 = 0

Reorder the terms:
-63 + -14x + x2 = 0

Solving
-63 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '63' to each side of the equation.
-63 + -14x + 63 + x2 = 0 + 63

Reorder the terms:
-63 + 63 + -14x + x2 = 0 + 63

Combine like terms: -63 + 63 = 0
0 + -14x + x2 = 0 + 63
-14x + x2 = 0 + 63

Combine like terms: 0 + 63 = 63
-14x + x2 = 63

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 = 63 + 49

Reorder the terms:
49 + -14x + x2 = 63 + 49

Combine like terms: 63 + 49 = 112
49 + -14x + x2 = 112

Factor a perfect square on the left side:
(x + -7)(x + -7) = 112

Calculate the square root of the right side: 10.583005244

Break this problem into two subproblems by setting 
(x + -7) equal to 10.583005244 and -10.583005244.


Subproblem 1
x + -7 = 10.583005244

Simplifying
x + -7 = 10.583005244

Reorder the terms:
-7 + x = 10.583005244

Solving
-7 + x = 10.583005244

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 = 10.583005244 + 7

Combine like terms: -7 + 7 = 0
0 + x = 10.583005244 + 7
x = 10.583005244 + 7

Combine like terms: 10.583005244 + 7 = 17.583005244
x = 17.583005244

Simplifying
x = 17.583005244


Subproblem 2
x + -7 = -10.583005244

Simplifying
x + -7 = -10.583005244

Reorder the terms:
-7 + x = -10.583005244

Solving
-7 + x = -10.583005244

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 = -10.583005244 + 7

Combine like terms: -7 + 7 = 0
0 + x = -10.583005244 + 7
x = -10.583005244 + 7

Combine like terms: -10.583005244 + 7 = -3.583005244
x = -3.583005244

Simplifying
x = -3.583005244


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.583005244, -3.583005244}

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