x^2-13x-280=0

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Solution for x^2-13x-280=0 equation: 


Simplifying
x2 + -13x + -280 = 0

Reorder the terms:
-280 + -13x + x2 = 0

Solving
-280 + -13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '280' to each side of the equation.
-280 + -13x + 280 + x2 = 0 + 280

Reorder the terms:
-280 + 280 + -13x + x2 = 0 + 280

Combine like terms: -280 + 280 = 0
0 + -13x + x2 = 0 + 280
-13x + x2 = 0 + 280

Combine like terms: 0 + 280 = 280
-13x + x2 = 280

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 280 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 280 + 42.25

Combine like terms: 280 + 42.25 = 322.25
42.25 + -13x + x2 = 322.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 322.25

Calculate the square root of the right side: 17.951323071

Break this problem into two subproblems by setting 
(x + -6.5) equal to 17.951323071 and -17.951323071.


Subproblem 1
x + -6.5 = 17.951323071

Simplifying
x + -6.5 = 17.951323071

Reorder the terms:
-6.5 + x = 17.951323071

Solving
-6.5 + x = 17.951323071

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 17.951323071 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 17.951323071 + 6.5
x = 17.951323071 + 6.5

Combine like terms: 17.951323071 + 6.5 = 24.451323071
x = 24.451323071

Simplifying
x = 24.451323071


Subproblem 2
x + -6.5 = -17.951323071

Simplifying
x + -6.5 = -17.951323071

Reorder the terms:
-6.5 + x = -17.951323071

Solving
-6.5 + x = -17.951323071

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -17.951323071 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -17.951323071 + 6.5
x = -17.951323071 + 6.5

Combine like terms: -17.951323071 + 6.5 = -11.451323071
x = -11.451323071

Simplifying
x = -11.451323071


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.451323071, -11.451323071}

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