x^2+5x-324=0

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Solution for x^2+5x-324=0 equation: 


Simplifying
x2 + 5x + -324 = 0

Reorder the terms:
-324 + 5x + x2 = 0

Solving
-324 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '324' to each side of the equation.
-324 + 5x + 324 + x2 = 0 + 324

Reorder the terms:
-324 + 324 + 5x + x2 = 0 + 324

Combine like terms: -324 + 324 = 0
0 + 5x + x2 = 0 + 324
5x + x2 = 0 + 324

Combine like terms: 0 + 324 = 324
5x + x2 = 324

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 = 324 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 324 + 6.25

Combine like terms: 324 + 6.25 = 330.25
6.25 + 5x + x2 = 330.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 330.25

Calculate the square root of the right side: 18.172781845

Break this problem into two subproblems by setting 
(x + 2.5) equal to 18.172781845 and -18.172781845.


Subproblem 1
x + 2.5 = 18.172781845

Simplifying
x + 2.5 = 18.172781845

Reorder the terms:
2.5 + x = 18.172781845

Solving
2.5 + x = 18.172781845

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 = 18.172781845 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 18.172781845 + -2.5
x = 18.172781845 + -2.5

Combine like terms: 18.172781845 + -2.5 = 15.672781845
x = 15.672781845

Simplifying
x = 15.672781845


Subproblem 2
x + 2.5 = -18.172781845

Simplifying
x + 2.5 = -18.172781845

Reorder the terms:
2.5 + x = -18.172781845

Solving
2.5 + x = -18.172781845

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 = -18.172781845 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -18.172781845 + -2.5
x = -18.172781845 + -2.5

Combine like terms: -18.172781845 + -2.5 = -20.672781845
x = -20.672781845

Simplifying
x = -20.672781845


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.672781845, -20.672781845}

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