x^2+25x-50=0

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Solution for x^2+25x-50=0 equation: 


Simplifying
x2 + 25x + -50 = 0

Reorder the terms:
-50 + 25x + x2 = 0

Solving
-50 + 25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + 25x + 50 + x2 = 0 + 50

Reorder the terms:
-50 + 50 + 25x + x2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + 25x + x2 = 0 + 50
25x + x2 = 0 + 50

Combine like terms: 0 + 50 = 50
25x + x2 = 50

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 = 50 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 50 + 156.25

Combine like terms: 50 + 156.25 = 206.25
156.25 + 25x + x2 = 206.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 206.25

Calculate the square root of the right side: 14.361406616

Break this problem into two subproblems by setting 
(x + 12.5) equal to 14.361406616 and -14.361406616.


Subproblem 1
x + 12.5 = 14.361406616

Simplifying
x + 12.5 = 14.361406616

Reorder the terms:
12.5 + x = 14.361406616

Solving
12.5 + x = 14.361406616

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 = 14.361406616 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 14.361406616 + -12.5
x = 14.361406616 + -12.5

Combine like terms: 14.361406616 + -12.5 = 1.861406616
x = 1.861406616

Simplifying
x = 1.861406616


Subproblem 2
x + 12.5 = -14.361406616

Simplifying
x + 12.5 = -14.361406616

Reorder the terms:
12.5 + x = -14.361406616

Solving
12.5 + x = -14.361406616

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 = -14.361406616 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -14.361406616 + -12.5
x = -14.361406616 + -12.5

Combine like terms: -14.361406616 + -12.5 = -26.861406616
x = -26.861406616

Simplifying
x = -26.861406616


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.861406616, -26.861406616}

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