x^2-28x-7=0

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Solution for x^2-28x-7=0 equation: 


Simplifying
x2 + -28x + -7 = 0

Reorder the terms:
-7 + -28x + x2 = 0

Solving
-7 + -28x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -28x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -28x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -28x + x2 = 0 + 7
-28x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-28x + x2 = 7

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 = 7 + 196

Reorder the terms:
196 + -28x + x2 = 7 + 196

Combine like terms: 7 + 196 = 203
196 + -28x + x2 = 203

Factor a perfect square on the left side:
(x + -14)(x + -14) = 203

Calculate the square root of the right side: 14.247806849

Break this problem into two subproblems by setting 
(x + -14) equal to 14.247806849 and -14.247806849.


Subproblem 1
x + -14 = 14.247806849

Simplifying
x + -14 = 14.247806849

Reorder the terms:
-14 + x = 14.247806849

Solving
-14 + x = 14.247806849

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 = 14.247806849 + 14

Combine like terms: -14 + 14 = 0
0 + x = 14.247806849 + 14
x = 14.247806849 + 14

Combine like terms: 14.247806849 + 14 = 28.247806849
x = 28.247806849

Simplifying
x = 28.247806849


Subproblem 2
x + -14 = -14.247806849

Simplifying
x + -14 = -14.247806849

Reorder the terms:
-14 + x = -14.247806849

Solving
-14 + x = -14.247806849

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 = -14.247806849 + 14

Combine like terms: -14 + 14 = 0
0 + x = -14.247806849 + 14
x = -14.247806849 + 14

Combine like terms: -14.247806849 + 14 = -0.247806849
x = -0.247806849

Simplifying
x = -0.247806849


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.247806849, -0.247806849}

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