x^2+0.3x-1.80=160

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Solution for x^2+0.3x-1.80=160 equation: 


Simplifying
x2 + 0.3x + -1.80 = 160

Reorder the terms:
-1.80 + 0.3x + x2 = 160

Solving
-1.80 + 0.3x + x2 = 160

Solving for variable 'x'.

Reorder the terms:
-1.80 + -160 + 0.3x + x2 = 160 + -160

Combine like terms: -1.80 + -160 = -161.8
-161.8 + 0.3x + x2 = 160 + -160

Combine like terms: 160 + -160 = 0
-161.8 + 0.3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '161.8' to each side of the equation.
-161.8 + 0.3x + 161.8 + x2 = 0 + 161.8

Reorder the terms:
-161.8 + 161.8 + 0.3x + x2 = 0 + 161.8

Combine like terms: -161.8 + 161.8 = 0.0
0.0 + 0.3x + x2 = 0 + 161.8
0.3x + x2 = 0 + 161.8

Combine like terms: 0 + 161.8 = 161.8
0.3x + x2 = 161.8

The x term is 0.3x.  Take half its coefficient (0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
0.3x + 0.0225 + x2 = 161.8 + 0.0225

Reorder the terms:
0.0225 + 0.3x + x2 = 161.8 + 0.0225

Combine like terms: 161.8 + 0.0225 = 161.8225
0.0225 + 0.3x + x2 = 161.8225

Factor a perfect square on the left side:
(x + 0.15)(x + 0.15) = 161.8225

Calculate the square root of the right side: 12.720947292

Break this problem into two subproblems by setting 
(x + 0.15) equal to 12.720947292 and -12.720947292.


Subproblem 1
x + 0.15 = 12.720947292

Simplifying
x + 0.15 = 12.720947292

Reorder the terms:
0.15 + x = 12.720947292

Solving
0.15 + x = 12.720947292

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = 12.720947292 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = 12.720947292 + -0.15
x = 12.720947292 + -0.15

Combine like terms: 12.720947292 + -0.15 = 12.570947292
x = 12.570947292

Simplifying
x = 12.570947292


Subproblem 2
x + 0.15 = -12.720947292

Simplifying
x + 0.15 = -12.720947292

Reorder the terms:
0.15 + x = -12.720947292

Solving
0.15 + x = -12.720947292

Solving for variable 'x'.

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

Add '-0.15' to each side of the equation.
0.15 + -0.15 + x = -12.720947292 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + x = -12.720947292 + -0.15
x = -12.720947292 + -0.15

Combine like terms: -12.720947292 + -0.15 = -12.870947292
x = -12.870947292

Simplifying
x = -12.870947292


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.570947292, -12.870947292}

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