x^2+3x=305

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Solution for x^2+3x=305 equation: 


Simplifying
x2 + 3x = 305

Reorder the terms:
3x + x2 = 305

Solving
3x + x2 = 305

Solving for variable 'x'.

Reorder the terms:
-305 + 3x + x2 = 305 + -305

Combine like terms: 305 + -305 = 0
-305 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '305' to each side of the equation.
-305 + 3x + 305 + x2 = 0 + 305

Reorder the terms:
-305 + 305 + 3x + x2 = 0 + 305

Combine like terms: -305 + 305 = 0
0 + 3x + x2 = 0 + 305
3x + x2 = 0 + 305

Combine like terms: 0 + 305 = 305
3x + x2 = 305

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 = 305 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 305 + 2.25

Combine like terms: 305 + 2.25 = 307.25
2.25 + 3x + x2 = 307.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 307.25

Calculate the square root of the right side: 17.528548143

Break this problem into two subproblems by setting 
(x + 1.5) equal to 17.528548143 and -17.528548143.


Subproblem 1
x + 1.5 = 17.528548143

Simplifying
x + 1.5 = 17.528548143

Reorder the terms:
1.5 + x = 17.528548143

Solving
1.5 + x = 17.528548143

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 = 17.528548143 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 17.528548143 + -1.5
x = 17.528548143 + -1.5

Combine like terms: 17.528548143 + -1.5 = 16.028548143
x = 16.028548143

Simplifying
x = 16.028548143


Subproblem 2
x + 1.5 = -17.528548143

Simplifying
x + 1.5 = -17.528548143

Reorder the terms:
1.5 + x = -17.528548143

Solving
1.5 + x = -17.528548143

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 = -17.528548143 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -17.528548143 + -1.5
x = -17.528548143 + -1.5

Combine like terms: -17.528548143 + -1.5 = -19.028548143
x = -19.028548143

Simplifying
x = -19.028548143


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.028548143, -19.028548143}

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