x^2+5x-390=0

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Solution for x^2+5x-390=0 equation: 


Simplifying
x2 + 5x + -390 = 0

Reorder the terms:
-390 + 5x + x2 = 0

Solving
-390 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '390' to each side of the equation.
-390 + 5x + 390 + x2 = 0 + 390

Reorder the terms:
-390 + 390 + 5x + x2 = 0 + 390

Combine like terms: -390 + 390 = 0
0 + 5x + x2 = 0 + 390
5x + x2 = 0 + 390

Combine like terms: 0 + 390 = 390
5x + x2 = 390

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 = 390 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 390 + 6.25

Combine like terms: 390 + 6.25 = 396.25
6.25 + 5x + x2 = 396.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 396.25

Calculate the square root of the right side: 19.906029237

Break this problem into two subproblems by setting 
(x + 2.5) equal to 19.906029237 and -19.906029237.


Subproblem 1
x + 2.5 = 19.906029237

Simplifying
x + 2.5 = 19.906029237

Reorder the terms:
2.5 + x = 19.906029237

Solving
2.5 + x = 19.906029237

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 = 19.906029237 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 19.906029237 + -2.5
x = 19.906029237 + -2.5

Combine like terms: 19.906029237 + -2.5 = 17.406029237
x = 17.406029237

Simplifying
x = 17.406029237


Subproblem 2
x + 2.5 = -19.906029237

Simplifying
x + 2.5 = -19.906029237

Reorder the terms:
2.5 + x = -19.906029237

Solving
2.5 + x = -19.906029237

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 = -19.906029237 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -19.906029237 + -2.5
x = -19.906029237 + -2.5

Combine like terms: -19.906029237 + -2.5 = -22.406029237
x = -22.406029237

Simplifying
x = -22.406029237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.406029237, -22.406029237}

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