189.028=2*3.14x^2+2*3.14x*2.7

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Solution for 189.028=2*3.14x^2+2*3.14x*2.7 equation: 


Simplifying
189.028 = 2 * 3.14x2 + 2 * 3.14x * 2.7

Multiply 2 * 3.14
189.028 = 6.28x2 + 2 * 3.14x * 2.7

Reorder the terms for easier multiplication:
189.028 = 6.28x2 + 2 * 3.14 * 2.7x

Multiply 2 * 3.14
189.028 = 6.28x2 + 6.28 * 2.7x

Multiply 6.28 * 2.7
189.028 = 6.28x2 + 16.956x

Reorder the terms:
189.028 = 16.956x + 6.28x2

Solving
189.028 = 16.956x + 6.28x2

Solving for variable 'x'.

Reorder the terms:
189.028 + -16.956x + -6.28x2 = 16.956x + -16.956x + 6.28x2 + -6.28x2

Combine like terms: 16.956x + -16.956x = 0.000
189.028 + -16.956x + -6.28x2 = 0.000 + 6.28x2 + -6.28x2
189.028 + -16.956x + -6.28x2 = 6.28x2 + -6.28x2

Combine like terms: 6.28x2 + -6.28x2 = 0.00
189.028 + -16.956x + -6.28x2 = 0.00

Begin completing the square.  Divide all terms by
-6.28 the coefficient of the squared term: 

Divide each side by '-6.28'.
-30.1 + 2.7x + x2 = 0

Move the constant term to the right:

Add '30.1' to each side of the equation.
-30.1 + 2.7x + 30.1 + x2 = 0 + 30.1

Reorder the terms:
-30.1 + 30.1 + 2.7x + x2 = 0 + 30.1

Combine like terms: -30.1 + 30.1 = 0.0
0.0 + 2.7x + x2 = 0 + 30.1
2.7x + x2 = 0 + 30.1

Combine like terms: 0 + 30.1 = 30.1
2.7x + x2 = 30.1

The x term is 2.7x.  Take half its coefficient (1.35).
Square it (1.8225) and add it to both sides.

Add '1.8225' to each side of the equation.
2.7x + 1.8225 + x2 = 30.1 + 1.8225

Reorder the terms:
1.8225 + 2.7x + x2 = 30.1 + 1.8225

Combine like terms: 30.1 + 1.8225 = 31.9225
1.8225 + 2.7x + x2 = 31.9225

Factor a perfect square on the left side:
(x + 1.35)(x + 1.35) = 31.9225

Calculate the square root of the right side: 5.65

Break this problem into two subproblems by setting 
(x + 1.35) equal to 5.65 and -5.65.


Subproblem 1
x + 1.35 = 5.65

Simplifying
x + 1.35 = 5.65

Reorder the terms:
1.35 + x = 5.65

Solving
1.35 + x = 5.65

Solving for variable 'x'.

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

Add '-1.35' to each side of the equation.
1.35 + -1.35 + x = 5.65 + -1.35

Combine like terms: 1.35 + -1.35 = 0.00
0.00 + x = 5.65 + -1.35
x = 5.65 + -1.35

Combine like terms: 5.65 + -1.35 = 4.3
x = 4.3

Simplifying
x = 4.3


Subproblem 2
x + 1.35 = -5.65

Simplifying
x + 1.35 = -5.65

Reorder the terms:
1.35 + x = -5.65

Solving
1.35 + x = -5.65

Solving for variable 'x'.

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

Add '-1.35' to each side of the equation.
1.35 + -1.35 + x = -5.65 + -1.35

Combine like terms: 1.35 + -1.35 = 0.00
0.00 + x = -5.65 + -1.35
x = -5.65 + -1.35

Combine like terms: -5.65 + -1.35 = -7
x = -7

Simplifying
x = -7


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.3, -7}

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