-3x^2+374x-2164=0

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Solution for -3x^2+374x-2164=0 equation:


Simplifying
-3x2 + 374x + -2164 = 0

Reorder the terms:
-2164 + 374x + -3x2 = 0

Solving
-2164 + 374x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
721.3333333 + -124.6666667x + x2 = 0

Move the constant term to the right:

Add '-721.3333333' to each side of the equation.
721.3333333 + -124.6666667x + -721.3333333 + x2 = 0 + -721.3333333

Reorder the terms:
721.3333333 + -721.3333333 + -124.6666667x + x2 = 0 + -721.3333333

Combine like terms: 721.3333333 + -721.3333333 = 0.0000000
0.0000000 + -124.6666667x + x2 = 0 + -721.3333333
-124.6666667x + x2 = 0 + -721.3333333

Combine like terms: 0 + -721.3333333 = -721.3333333
-124.6666667x + x2 = -721.3333333

The x term is -124.6666667x.  Take half its coefficient (-62.33333335).
Square it (3885.444447) and add it to both sides.

Add '3885.444447' to each side of the equation.
-124.6666667x + 3885.444447 + x2 = -721.3333333 + 3885.444447

Reorder the terms:
3885.444447 + -124.6666667x + x2 = -721.3333333 + 3885.444447

Combine like terms: -721.3333333 + 3885.444447 = 3164.1111137
3885.444447 + -124.6666667x + x2 = 3164.1111137

Factor a perfect square on the left side:
(x + -62.33333335)(x + -62.33333335) = 3164.1111137

Calculate the square root of the right side: 56.25043212

Break this problem into two subproblems by setting 
(x + -62.33333335) equal to 56.25043212 and -56.25043212.


Subproblem 1
x + -62.33333335 = 56.25043212

Simplifying
x + -62.33333335 = 56.25043212

Reorder the terms:
-62.33333335 + x = 56.25043212

Solving
-62.33333335 + x = 56.25043212

Solving for variable 'x'.

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

Add '62.33333335' to each side of the equation.
-62.33333335 + 62.33333335 + x = 56.25043212 + 62.33333335

Combine like terms: -62.33333335 + 62.33333335 = 0.00000000
0.00000000 + x = 56.25043212 + 62.33333335
x = 56.25043212 + 62.33333335

Combine like terms: 56.25043212 + 62.33333335 = 118.58376547
x = 118.58376547

Simplifying
x = 118.58376547


Subproblem 2
x + -62.33333335 = -56.25043212

Simplifying
x + -62.33333335 = -56.25043212

Reorder the terms:
-62.33333335 + x = -56.25043212

Solving
-62.33333335 + x = -56.25043212

Solving for variable 'x'.

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

Add '62.33333335' to each side of the equation.
-62.33333335 + 62.33333335 + x = -56.25043212 + 62.33333335

Combine like terms: -62.33333335 + 62.33333335 = 0.00000000
0.00000000 + x = -56.25043212 + 62.33333335
x = -56.25043212 + 62.33333335

Combine like terms: -56.25043212 + 62.33333335 = 6.08290123
x = 6.08290123

Simplifying
x = 6.08290123


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {118.58376547, 6.08290123}

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