x^2+3x-54.59815=0

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Solution for x^2+3x-54.59815=0 equation: 


Simplifying
x2 + 3x + -54.59815 = 0

Reorder the terms:
-54.59815 + 3x + x2 = 0

Solving
-54.59815 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '54.59815' to each side of the equation.
-54.59815 + 3x + 54.59815 + x2 = 0 + 54.59815

Reorder the terms:
-54.59815 + 54.59815 + 3x + x2 = 0 + 54.59815

Combine like terms: -54.59815 + 54.59815 = 0.00000
0.00000 + 3x + x2 = 0 + 54.59815
3x + x2 = 0 + 54.59815

Combine like terms: 0 + 54.59815 = 54.59815
3x + x2 = 54.59815

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 54.59815 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 54.59815 + 2.25

Combine like terms: 54.59815 + 2.25 = 56.84815
2.25 + 3x + x2 = 56.84815

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 56.84815

Calculate the square root of the right side: 7.539771217

Break this problem into two subproblems by setting 
(x + 1.5) equal to 7.539771217 and -7.539771217.


Subproblem 1
x + 1.5 = 7.539771217

Simplifying
x + 1.5 = 7.539771217

Reorder the terms:
1.5 + x = 7.539771217

Solving
1.5 + x = 7.539771217

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 7.539771217 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 7.539771217 + -1.5
x = 7.539771217 + -1.5

Combine like terms: 7.539771217 + -1.5 = 6.039771217
x = 6.039771217

Simplifying
x = 6.039771217


Subproblem 2
x + 1.5 = -7.539771217

Simplifying
x + 1.5 = -7.539771217

Reorder the terms:
1.5 + x = -7.539771217

Solving
1.5 + x = -7.539771217

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -7.539771217 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -7.539771217 + -1.5
x = -7.539771217 + -1.5

Combine like terms: -7.539771217 + -1.5 = -9.039771217
x = -9.039771217

Simplifying
x = -9.039771217


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.039771217, -9.039771217}

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