-3x^2-25x+6=0

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Solution for -3x^2-25x+6=0 equation: 


Simplifying
-3x2 + -25x + 6 = 0

Reorder the terms:
6 + -25x + -3x2 = 0

Solving
6 + -25x + -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'.
-2 + 8.333333333x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 8.333333333x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 8.333333333x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 8.333333333x + x2 = 0 + 2
8.333333333x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
8.333333333x + x2 = 2

The x term is 8.333333333x.  Take half its coefficient (4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
8.333333333x + 17.36111111 + x2 = 2 + 17.36111111

Reorder the terms:
17.36111111 + 8.333333333x + x2 = 2 + 17.36111111

Combine like terms: 2 + 17.36111111 = 19.36111111
17.36111111 + 8.333333333x + x2 = 19.36111111

Factor a perfect square on the left side:
(x + 4.166666667)(x + 4.166666667) = 19.36111111

Calculate the square root of the right side: 4.400126261

Break this problem into two subproblems by setting 
(x + 4.166666667) equal to 4.400126261 and -4.400126261.


Subproblem 1
x + 4.166666667 = 4.400126261

Simplifying
x + 4.166666667 = 4.400126261

Reorder the terms:
4.166666667 + x = 4.400126261

Solving
4.166666667 + x = 4.400126261

Solving for variable 'x'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + x = 4.400126261 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = 4.400126261 + -4.166666667
x = 4.400126261 + -4.166666667

Combine like terms: 4.400126261 + -4.166666667 = 0.233459594
x = 0.233459594

Simplifying
x = 0.233459594


Subproblem 2
x + 4.166666667 = -4.400126261

Simplifying
x + 4.166666667 = -4.400126261

Reorder the terms:
4.166666667 + x = -4.400126261

Solving
4.166666667 + x = -4.400126261

Solving for variable 'x'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + x = -4.400126261 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = -4.400126261 + -4.166666667
x = -4.400126261 + -4.166666667

Combine like terms: -4.400126261 + -4.166666667 = -8.566792928
x = -8.566792928

Simplifying
x = -8.566792928


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.233459594, -8.566792928}

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