x^2+3x=65.7

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Solution for x^2+3x=65.7 equation: 


Simplifying
x2 + 3x = 65.7

Reorder the terms:
3x + x2 = 65.7

Solving
3x + x2 = 65.7

Solving for variable 'x'.

Reorder the terms:
-65.7 + 3x + x2 = 65.7 + -65.7

Combine like terms: 65.7 + -65.7 = 0.0
-65.7 + 3x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '65.7' to each side of the equation.
-65.7 + 3x + 65.7 + x2 = 0.0 + 65.7

Reorder the terms:
-65.7 + 65.7 + 3x + x2 = 0.0 + 65.7

Combine like terms: -65.7 + 65.7 = 0.0
0.0 + 3x + x2 = 0.0 + 65.7
3x + x2 = 0.0 + 65.7

Combine like terms: 0.0 + 65.7 = 65.7
3x + x2 = 65.7

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 = 65.7 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 65.7 + 2.25

Combine like terms: 65.7 + 2.25 = 67.95
2.25 + 3x + x2 = 67.95

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 67.95

Calculate the square root of the right side: 8.243178998

Break this problem into two subproblems by setting 
(x + 1.5) equal to 8.243178998 and -8.243178998.


Subproblem 1
x + 1.5 = 8.243178998

Simplifying
x + 1.5 = 8.243178998

Reorder the terms:
1.5 + x = 8.243178998

Solving
1.5 + x = 8.243178998

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 = 8.243178998 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 8.243178998 + -1.5
x = 8.243178998 + -1.5

Combine like terms: 8.243178998 + -1.5 = 6.743178998
x = 6.743178998

Simplifying
x = 6.743178998


Subproblem 2
x + 1.5 = -8.243178998

Simplifying
x + 1.5 = -8.243178998

Reorder the terms:
1.5 + x = -8.243178998

Solving
1.5 + x = -8.243178998

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 = -8.243178998 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -8.243178998 + -1.5
x = -8.243178998 + -1.5

Combine like terms: -8.243178998 + -1.5 = -9.743178998
x = -9.743178998

Simplifying
x = -9.743178998


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.743178998, -9.743178998}

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