4x^2-37x-119=0

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Solution for 4x^2-37x-119=0 equation: 


Simplifying
4x2 + -37x + -119 = 0

Reorder the terms:
-119 + -37x + 4x2 = 0

Solving
-119 + -37x + 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'.
-29.75 + -9.25x + x2 = 0

Move the constant term to the right:

Add '29.75' to each side of the equation.
-29.75 + -9.25x + 29.75 + x2 = 0 + 29.75

Reorder the terms:
-29.75 + 29.75 + -9.25x + x2 = 0 + 29.75

Combine like terms: -29.75 + 29.75 = 0.00
0.00 + -9.25x + x2 = 0 + 29.75
-9.25x + x2 = 0 + 29.75

Combine like terms: 0 + 29.75 = 29.75
-9.25x + x2 = 29.75

The x term is -9.25x.  Take half its coefficient (-4.625).
Square it (21.390625) and add it to both sides.

Add '21.390625' to each side of the equation.
-9.25x + 21.390625 + x2 = 29.75 + 21.390625

Reorder the terms:
21.390625 + -9.25x + x2 = 29.75 + 21.390625

Combine like terms: 29.75 + 21.390625 = 51.140625
21.390625 + -9.25x + x2 = 51.140625

Factor a perfect square on the left side:
(x + -4.625)(x + -4.625) = 51.140625

Calculate the square root of the right side: 7.15126737

Break this problem into two subproblems by setting 
(x + -4.625) equal to 7.15126737 and -7.15126737.


Subproblem 1
x + -4.625 = 7.15126737

Simplifying
x + -4.625 = 7.15126737

Reorder the terms:
-4.625 + x = 7.15126737

Solving
-4.625 + x = 7.15126737

Solving for variable 'x'.

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

Add '4.625' to each side of the equation.
-4.625 + 4.625 + x = 7.15126737 + 4.625

Combine like terms: -4.625 + 4.625 = 0.000
0.000 + x = 7.15126737 + 4.625
x = 7.15126737 + 4.625

Combine like terms: 7.15126737 + 4.625 = 11.77626737
x = 11.77626737

Simplifying
x = 11.77626737


Subproblem 2
x + -4.625 = -7.15126737

Simplifying
x + -4.625 = -7.15126737

Reorder the terms:
-4.625 + x = -7.15126737

Solving
-4.625 + x = -7.15126737

Solving for variable 'x'.

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

Add '4.625' to each side of the equation.
-4.625 + 4.625 + x = -7.15126737 + 4.625

Combine like terms: -4.625 + 4.625 = 0.000
0.000 + x = -7.15126737 + 4.625
x = -7.15126737 + 4.625

Combine like terms: -7.15126737 + 4.625 = -2.52626737
x = -2.52626737

Simplifying
x = -2.52626737


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.77626737, -2.52626737}

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