x^2-28x-102=0

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Solution for x^2-28x-102=0 equation: 


Simplifying
x2 + -28x + -102 = 0

Reorder the terms:
-102 + -28x + x2 = 0

Solving
-102 + -28x + 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 + -28x + 102 + x2 = 0 + 102

Reorder the terms:
-102 + 102 + -28x + x2 = 0 + 102

Combine like terms: -102 + 102 = 0
0 + -28x + x2 = 0 + 102
-28x + x2 = 0 + 102

Combine like terms: 0 + 102 = 102
-28x + x2 = 102

The x term is -28x.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28x + 196 + x2 = 102 + 196

Reorder the terms:
196 + -28x + x2 = 102 + 196

Combine like terms: 102 + 196 = 298
196 + -28x + x2 = 298

Factor a perfect square on the left side:
(x + -14)(x + -14) = 298

Calculate the square root of the right side: 17.262676502

Break this problem into two subproblems by setting 
(x + -14) equal to 17.262676502 and -17.262676502.


Subproblem 1
x + -14 = 17.262676502

Simplifying
x + -14 = 17.262676502

Reorder the terms:
-14 + x = 17.262676502

Solving
-14 + x = 17.262676502

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '14' to each side of the equation.
-14 + 14 + x = 17.262676502 + 14

Combine like terms: -14 + 14 = 0
0 + x = 17.262676502 + 14
x = 17.262676502 + 14

Combine like terms: 17.262676502 + 14 = 31.262676502
x = 31.262676502

Simplifying
x = 31.262676502


Subproblem 2
x + -14 = -17.262676502

Simplifying
x + -14 = -17.262676502

Reorder the terms:
-14 + x = -17.262676502

Solving
-14 + x = -17.262676502

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '14' to each side of the equation.
-14 + 14 + x = -17.262676502 + 14

Combine like terms: -14 + 14 = 0
0 + x = -17.262676502 + 14
x = -17.262676502 + 14

Combine like terms: -17.262676502 + 14 = -3.262676502
x = -3.262676502

Simplifying
x = -3.262676502


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {31.262676502, -3.262676502}

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