x^2+3x=8.33333333

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Solution for x^2+3x=8.33333333 equation: 


Simplifying
x2 + 3x = 8.33333333

Reorder the terms:
3x + x2 = 8.33333333

Solving
3x + x2 = 8.33333333

Solving for variable 'x'.

Reorder the terms:
-8.33333333 + 3x + x2 = 8.33333333 + -8.33333333

Combine like terms: 8.33333333 + -8.33333333 = 0.00000000
-8.33333333 + 3x + x2 = 0.00000000

Begin completing the square.

Move the constant term to the right:

Add '8.33333333' to each side of the equation.
-8.33333333 + 3x + 8.33333333 + x2 = 0.00000000 + 8.33333333

Reorder the terms:
-8.33333333 + 8.33333333 + 3x + x2 = 0.00000000 + 8.33333333

Combine like terms: -8.33333333 + 8.33333333 = 0.00000000
0.00000000 + 3x + x2 = 0.00000000 + 8.33333333
3x + x2 = 0.00000000 + 8.33333333

Combine like terms: 0.00000000 + 8.33333333 = 8.33333333
3x + x2 = 8.33333333

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 = 8.33333333 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 8.33333333 + 2.25

Combine like terms: 8.33333333 + 2.25 = 10.58333333
2.25 + 3x + x2 = 10.58333333

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 10.58333333

Calculate the square root of the right side: 3.253203549

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.253203549 and -3.253203549.


Subproblem 1
x + 1.5 = 3.253203549

Simplifying
x + 1.5 = 3.253203549

Reorder the terms:
1.5 + x = 3.253203549

Solving
1.5 + x = 3.253203549

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 = 3.253203549 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 3.253203549 + -1.5
x = 3.253203549 + -1.5

Combine like terms: 3.253203549 + -1.5 = 1.753203549
x = 1.753203549

Simplifying
x = 1.753203549


Subproblem 2
x + 1.5 = -3.253203549

Simplifying
x + 1.5 = -3.253203549

Reorder the terms:
1.5 + x = -3.253203549

Solving
1.5 + x = -3.253203549

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 = -3.253203549 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -3.253203549 + -1.5
x = -3.253203549 + -1.5

Combine like terms: -3.253203549 + -1.5 = -4.753203549
x = -4.753203549

Simplifying
x = -4.753203549


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.753203549, -4.753203549}

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