x^2+14x-102=0

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Solution for x^2+14x-102=0 equation: 


Simplifying
x2 + 14x + -102 = 0

Reorder the terms:
-102 + 14x + x2 = 0

Solving
-102 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '102' to each side of the equation.
-102 + 14x + 102 + x2 = 0 + 102

Reorder the terms:
-102 + 102 + 14x + x2 = 0 + 102

Combine like terms: -102 + 102 = 0
0 + 14x + x2 = 0 + 102
14x + x2 = 0 + 102

Combine like terms: 0 + 102 = 102
14x + x2 = 102

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 = 102 + 49

Reorder the terms:
49 + 14x + x2 = 102 + 49

Combine like terms: 102 + 49 = 151
49 + 14x + x2 = 151

Factor a perfect square on the left side:
(x + 7)(x + 7) = 151

Calculate the square root of the right side: 12.288205727

Break this problem into two subproblems by setting 
(x + 7) equal to 12.288205727 and -12.288205727.


Subproblem 1
x + 7 = 12.288205727

Simplifying
x + 7 = 12.288205727

Reorder the terms:
7 + x = 12.288205727

Solving
7 + x = 12.288205727

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 = 12.288205727 + -7

Combine like terms: 7 + -7 = 0
0 + x = 12.288205727 + -7
x = 12.288205727 + -7

Combine like terms: 12.288205727 + -7 = 5.288205727
x = 5.288205727

Simplifying
x = 5.288205727


Subproblem 2
x + 7 = -12.288205727

Simplifying
x + 7 = -12.288205727

Reorder the terms:
7 + x = -12.288205727

Solving
7 + x = -12.288205727

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 = -12.288205727 + -7

Combine like terms: 7 + -7 = 0
0 + x = -12.288205727 + -7
x = -12.288205727 + -7

Combine like terms: -12.288205727 + -7 = -19.288205727
x = -19.288205727

Simplifying
x = -19.288205727


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.288205727, -19.288205727}

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