x^2+19x-1216=0

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Solution for x^2+19x-1216=0 equation: 


Simplifying
x2 + 19x + -1216 = 0

Reorder the terms:
-1216 + 19x + x2 = 0

Solving
-1216 + 19x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1216' to each side of the equation.
-1216 + 19x + 1216 + x2 = 0 + 1216

Reorder the terms:
-1216 + 1216 + 19x + x2 = 0 + 1216

Combine like terms: -1216 + 1216 = 0
0 + 19x + x2 = 0 + 1216
19x + x2 = 0 + 1216

Combine like terms: 0 + 1216 = 1216
19x + x2 = 1216

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = 1216 + 90.25

Reorder the terms:
90.25 + 19x + x2 = 1216 + 90.25

Combine like terms: 1216 + 90.25 = 1306.25
90.25 + 19x + x2 = 1306.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 1306.25

Calculate the square root of the right side: 36.142080737

Break this problem into two subproblems by setting 
(x + 9.5) equal to 36.142080737 and -36.142080737.


Subproblem 1
x + 9.5 = 36.142080737

Simplifying
x + 9.5 = 36.142080737

Reorder the terms:
9.5 + x = 36.142080737

Solving
9.5 + x = 36.142080737

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = 36.142080737 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 36.142080737 + -9.5
x = 36.142080737 + -9.5

Combine like terms: 36.142080737 + -9.5 = 26.642080737
x = 26.642080737

Simplifying
x = 26.642080737


Subproblem 2
x + 9.5 = -36.142080737

Simplifying
x + 9.5 = -36.142080737

Reorder the terms:
9.5 + x = -36.142080737

Solving
9.5 + x = -36.142080737

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = -36.142080737 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -36.142080737 + -9.5
x = -36.142080737 + -9.5

Combine like terms: -36.142080737 + -9.5 = -45.642080737
x = -45.642080737

Simplifying
x = -45.642080737


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.642080737, -45.642080737}

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