x^2-5x-725=0

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Solution for x^2-5x-725=0 equation: 


Simplifying
x2 + -5x + -725 = 0

Reorder the terms:
-725 + -5x + x2 = 0

Solving
-725 + -5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '725' to each side of the equation.
-725 + -5x + 725 + x2 = 0 + 725

Reorder the terms:
-725 + 725 + -5x + x2 = 0 + 725

Combine like terms: -725 + 725 = 0
0 + -5x + x2 = 0 + 725
-5x + x2 = 0 + 725

Combine like terms: 0 + 725 = 725
-5x + x2 = 725

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 725 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 725 + 6.25

Combine like terms: 725 + 6.25 = 731.25
6.25 + -5x + x2 = 731.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 731.25

Calculate the square root of the right side: 27.041634566

Break this problem into two subproblems by setting 
(x + -2.5) equal to 27.041634566 and -27.041634566.


Subproblem 1
x + -2.5 = 27.041634566

Simplifying
x + -2.5 = 27.041634566

Reorder the terms:
-2.5 + x = 27.041634566

Solving
-2.5 + x = 27.041634566

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 27.041634566 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 27.041634566 + 2.5
x = 27.041634566 + 2.5

Combine like terms: 27.041634566 + 2.5 = 29.541634566
x = 29.541634566

Simplifying
x = 29.541634566


Subproblem 2
x + -2.5 = -27.041634566

Simplifying
x + -2.5 = -27.041634566

Reorder the terms:
-2.5 + x = -27.041634566

Solving
-2.5 + x = -27.041634566

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -27.041634566 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -27.041634566 + 2.5
x = -27.041634566 + 2.5

Combine like terms: -27.041634566 + 2.5 = -24.541634566
x = -24.541634566

Simplifying
x = -24.541634566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {29.541634566, -24.541634566}

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