x^2-28x-68=0

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Solution for x^2-28x-68=0 equation: 


Simplifying
x2 + -28x + -68 = 0

Reorder the terms:
-68 + -28x + x2 = 0

Solving
-68 + -28x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '68' to each side of the equation.
-68 + -28x + 68 + x2 = 0 + 68

Reorder the terms:
-68 + 68 + -28x + x2 = 0 + 68

Combine like terms: -68 + 68 = 0
0 + -28x + x2 = 0 + 68
-28x + x2 = 0 + 68

Combine like terms: 0 + 68 = 68
-28x + x2 = 68

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 = 68 + 196

Reorder the terms:
196 + -28x + x2 = 68 + 196

Combine like terms: 68 + 196 = 264
196 + -28x + x2 = 264

Factor a perfect square on the left side:
(x + -14)(x + -14) = 264

Calculate the square root of the right side: 16.248076809

Break this problem into two subproblems by setting 
(x + -14) equal to 16.248076809 and -16.248076809.


Subproblem 1
x + -14 = 16.248076809

Simplifying
x + -14 = 16.248076809

Reorder the terms:
-14 + x = 16.248076809

Solving
-14 + x = 16.248076809

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 = 16.248076809 + 14

Combine like terms: -14 + 14 = 0
0 + x = 16.248076809 + 14
x = 16.248076809 + 14

Combine like terms: 16.248076809 + 14 = 30.248076809
x = 30.248076809

Simplifying
x = 30.248076809


Subproblem 2
x + -14 = -16.248076809

Simplifying
x + -14 = -16.248076809

Reorder the terms:
-14 + x = -16.248076809

Solving
-14 + x = -16.248076809

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 = -16.248076809 + 14

Combine like terms: -14 + 14 = 0
0 + x = -16.248076809 + 14
x = -16.248076809 + 14

Combine like terms: -16.248076809 + 14 = -2.248076809
x = -2.248076809

Simplifying
x = -2.248076809


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {30.248076809, -2.248076809}

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