x^2+25x-305=0

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Solution for x^2+25x-305=0 equation: 


Simplifying
x2 + 25x + -305 = 0

Reorder the terms:
-305 + 25x + x2 = 0

Solving
-305 + 25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '305' to each side of the equation.
-305 + 25x + 305 + x2 = 0 + 305

Reorder the terms:
-305 + 305 + 25x + x2 = 0 + 305

Combine like terms: -305 + 305 = 0
0 + 25x + x2 = 0 + 305
25x + x2 = 0 + 305

Combine like terms: 0 + 305 = 305
25x + x2 = 305

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 = 305 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 305 + 156.25

Combine like terms: 305 + 156.25 = 461.25
156.25 + 25x + x2 = 461.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 461.25

Calculate the square root of the right side: 21.476731595

Break this problem into two subproblems by setting 
(x + 12.5) equal to 21.476731595 and -21.476731595.


Subproblem 1
x + 12.5 = 21.476731595

Simplifying
x + 12.5 = 21.476731595

Reorder the terms:
12.5 + x = 21.476731595

Solving
12.5 + x = 21.476731595

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 = 21.476731595 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 21.476731595 + -12.5
x = 21.476731595 + -12.5

Combine like terms: 21.476731595 + -12.5 = 8.976731595
x = 8.976731595

Simplifying
x = 8.976731595


Subproblem 2
x + 12.5 = -21.476731595

Simplifying
x + 12.5 = -21.476731595

Reorder the terms:
12.5 + x = -21.476731595

Solving
12.5 + x = -21.476731595

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 = -21.476731595 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -21.476731595 + -12.5
x = -21.476731595 + -12.5

Combine like terms: -21.476731595 + -12.5 = -33.976731595
x = -33.976731595

Simplifying
x = -33.976731595


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.976731595, -33.976731595}

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