x^2+5x-729=0

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Solution for x^2+5x-729=0 equation: 


Simplifying
x2 + 5x + -729 = 0

Reorder the terms:
-729 + 5x + x2 = 0

Solving
-729 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '729' to each side of the equation.
-729 + 5x + 729 + x2 = 0 + 729

Reorder the terms:
-729 + 729 + 5x + x2 = 0 + 729

Combine like terms: -729 + 729 = 0
0 + 5x + x2 = 0 + 729
5x + x2 = 0 + 729

Combine like terms: 0 + 729 = 729
5x + x2 = 729

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 = 729 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 729 + 6.25

Combine like terms: 729 + 6.25 = 735.25
6.25 + 5x + x2 = 735.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 735.25

Calculate the square root of the right side: 27.115493726

Break this problem into two subproblems by setting 
(x + 2.5) equal to 27.115493726 and -27.115493726.


Subproblem 1
x + 2.5 = 27.115493726

Simplifying
x + 2.5 = 27.115493726

Reorder the terms:
2.5 + x = 27.115493726

Solving
2.5 + x = 27.115493726

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 = 27.115493726 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 27.115493726 + -2.5
x = 27.115493726 + -2.5

Combine like terms: 27.115493726 + -2.5 = 24.615493726
x = 24.615493726

Simplifying
x = 24.615493726


Subproblem 2
x + 2.5 = -27.115493726

Simplifying
x + 2.5 = -27.115493726

Reorder the terms:
2.5 + x = -27.115493726

Solving
2.5 + x = -27.115493726

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 = -27.115493726 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -27.115493726 + -2.5
x = -27.115493726 + -2.5

Combine like terms: -27.115493726 + -2.5 = -29.615493726
x = -29.615493726

Simplifying
x = -29.615493726


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.615493726, -29.615493726}

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