4x^2-19x-100=0

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Solution for 4x^2-19x-100=0 equation: 


Simplifying
4x2 + -19x + -100 = 0

Reorder the terms:
-100 + -19x + 4x2 = 0

Solving
-100 + -19x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-25 + -4.75x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -4.75x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -4.75x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -4.75x + x2 = 0 + 25
-4.75x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-4.75x + x2 = 25

The x term is -4.75x.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75x + 5.640625 + x2 = 25 + 5.640625

Reorder the terms:
5.640625 + -4.75x + x2 = 25 + 5.640625

Combine like terms: 25 + 5.640625 = 30.640625
5.640625 + -4.75x + x2 = 30.640625

Factor a perfect square on the left side:
(x + -2.375)(x + -2.375) = 30.640625

Calculate the square root of the right side: 5.535397456

Break this problem into two subproblems by setting 
(x + -2.375) equal to 5.535397456 and -5.535397456.


Subproblem 1
x + -2.375 = 5.535397456

Simplifying
x + -2.375 = 5.535397456

Reorder the terms:
-2.375 + x = 5.535397456

Solving
-2.375 + x = 5.535397456

Solving for variable 'x'.

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

Add '2.375' to each side of the equation.
-2.375 + 2.375 + x = 5.535397456 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + x = 5.535397456 + 2.375
x = 5.535397456 + 2.375

Combine like terms: 5.535397456 + 2.375 = 7.910397456
x = 7.910397456

Simplifying
x = 7.910397456


Subproblem 2
x + -2.375 = -5.535397456

Simplifying
x + -2.375 = -5.535397456

Reorder the terms:
-2.375 + x = -5.535397456

Solving
-2.375 + x = -5.535397456

Solving for variable 'x'.

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

Add '2.375' to each side of the equation.
-2.375 + 2.375 + x = -5.535397456 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + x = -5.535397456 + 2.375
x = -5.535397456 + 2.375

Combine like terms: -5.535397456 + 2.375 = -3.160397456
x = -3.160397456

Simplifying
x = -3.160397456


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.910397456, -3.160397456}

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