0=x^2+25x+6

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


Simplifying
0 = x2 + 25x + 6

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

Solving
0 = 6 + 25x + x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + -25x + -1x2 = 6 + 25x + x2 + -6 + -25x + -1x2

Reorder the terms:
-6 + -25x + -1x2 = 6 + -6 + 25x + -25x + x2 + -1x2

Combine like terms: 6 + -6 = 0
-6 + -25x + -1x2 = 0 + 25x + -25x + x2 + -1x2
-6 + -25x + -1x2 = 25x + -25x + x2 + -1x2

Combine like terms: 25x + -25x = 0
-6 + -25x + -1x2 = 0 + x2 + -1x2
-6 + -25x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + -25x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 25x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(6 + 25x + x2)' equal to zero and attempt to solve:

Simplifying
6 + 25x + x2 = 0

Solving
6 + 25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 25x + -6 + x2 = 0 + -6

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

Combine like terms: 6 + -6 = 0
0 + 25x + x2 = 0 + -6
25x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
25x + x2 = -6

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = -6 + 156.25

Reorder the terms:
156.25 + 25x + x2 = -6 + 156.25

Combine like terms: -6 + 156.25 = 150.25
156.25 + 25x + x2 = 150.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 150.25

Calculate the square root of the right side: 12.257650672

Break this problem into two subproblems by setting 
(x + 12.5) equal to 12.257650672 and -12.257650672.


Subproblem 1
x + 12.5 = 12.257650672

Simplifying
x + 12.5 = 12.257650672

Reorder the terms:
12.5 + x = 12.257650672

Solving
12.5 + x = 12.257650672

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 12.257650672 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 12.257650672 + -12.5
x = 12.257650672 + -12.5

Combine like terms: 12.257650672 + -12.5 = -0.242349328
x = -0.242349328

Simplifying
x = -0.242349328


Subproblem 2
x + 12.5 = -12.257650672

Simplifying
x + 12.5 = -12.257650672

Reorder the terms:
12.5 + x = -12.257650672

Solving
12.5 + x = -12.257650672

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -12.257650672 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -12.257650672 + -12.5
x = -12.257650672 + -12.5

Combine like terms: -12.257650672 + -12.5 = -24.757650672
x = -24.757650672

Simplifying
x = -24.757650672


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.242349328, -24.757650672}
Solution
x = {-0.242349328, -24.757650672}

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