x^2-19x-75=0

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Solution for x^2-19x-75=0 equation: 


Simplifying
x2 + -19x + -75 = 0

Reorder the terms:
-75 + -19x + x2 = 0

Solving
-75 + -19x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + -19x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + -19x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + -19x + x2 = 0 + 75
-19x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
-19x + x2 = 75

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 = 75 + 90.25

Reorder the terms:
90.25 + -19x + x2 = 75 + 90.25

Combine like terms: 75 + 90.25 = 165.25
90.25 + -19x + x2 = 165.25

Factor a perfect square on the left side:
(x + -9.5)(x + -9.5) = 165.25

Calculate the square root of the right side: 12.854960132

Break this problem into two subproblems by setting 
(x + -9.5) equal to 12.854960132 and -12.854960132.


Subproblem 1
x + -9.5 = 12.854960132

Simplifying
x + -9.5 = 12.854960132

Reorder the terms:
-9.5 + x = 12.854960132

Solving
-9.5 + x = 12.854960132

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 = 12.854960132 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = 12.854960132 + 9.5
x = 12.854960132 + 9.5

Combine like terms: 12.854960132 + 9.5 = 22.354960132
x = 22.354960132

Simplifying
x = 22.354960132


Subproblem 2
x + -9.5 = -12.854960132

Simplifying
x + -9.5 = -12.854960132

Reorder the terms:
-9.5 + x = -12.854960132

Solving
-9.5 + x = -12.854960132

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 = -12.854960132 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + x = -12.854960132 + 9.5
x = -12.854960132 + 9.5

Combine like terms: -12.854960132 + 9.5 = -3.354960132
x = -3.354960132

Simplifying
x = -3.354960132


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.354960132, -3.354960132}

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