6x^2-25x-4=0

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Solution for 6x^2-25x-4=0 equation: 


Simplifying
6x2 + -25x + -4 = 0

Reorder the terms:
-4 + -25x + 6x2 = 0

Solving
-4 + -25x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-0.6666666667 + -4.166666667x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + -4.166666667x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + -4.166666667x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + -4.166666667x + x2 = 0 + 0.6666666667
-4.166666667x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
-4.166666667x + x2 = 0.6666666667

The x term is -4.166666667x.  Take half its coefficient (-2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
-4.166666667x + 4.340277781 + x2 = 0.6666666667 + 4.340277781

Reorder the terms:
4.340277781 + -4.166666667x + x2 = 0.6666666667 + 4.340277781

Combine like terms: 0.6666666667 + 4.340277781 = 5.0069444477
4.340277781 + -4.166666667x + x2 = 5.0069444477

Factor a perfect square on the left side:
(x + -2.083333334)(x + -2.083333334) = 5.0069444477

Calculate the square root of the right side: 2.237620264

Break this problem into two subproblems by setting 
(x + -2.083333334) equal to 2.237620264 and -2.237620264.


Subproblem 1
x + -2.083333334 = 2.237620264

Simplifying
x + -2.083333334 = 2.237620264

Reorder the terms:
-2.083333334 + x = 2.237620264

Solving
-2.083333334 + x = 2.237620264

Solving for variable 'x'.

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

Add '2.083333334' to each side of the equation.
-2.083333334 + 2.083333334 + x = 2.237620264 + 2.083333334

Combine like terms: -2.083333334 + 2.083333334 = 0.000000000
0.000000000 + x = 2.237620264 + 2.083333334
x = 2.237620264 + 2.083333334

Combine like terms: 2.237620264 + 2.083333334 = 4.320953598
x = 4.320953598

Simplifying
x = 4.320953598


Subproblem 2
x + -2.083333334 = -2.237620264

Simplifying
x + -2.083333334 = -2.237620264

Reorder the terms:
-2.083333334 + x = -2.237620264

Solving
-2.083333334 + x = -2.237620264

Solving for variable 'x'.

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

Add '2.083333334' to each side of the equation.
-2.083333334 + 2.083333334 + x = -2.237620264 + 2.083333334

Combine like terms: -2.083333334 + 2.083333334 = 0.000000000
0.000000000 + x = -2.237620264 + 2.083333334
x = -2.237620264 + 2.083333334

Combine like terms: -2.237620264 + 2.083333334 = -0.15428693
x = -0.15428693

Simplifying
x = -0.15428693


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.320953598, -0.15428693}

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