-2.11=3x^2-28x+61

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Solution for -2.11=3x^2-28x+61 equation: 


Simplifying
-2.11 = 3x2 + -28x + 61

Reorder the terms:
-2.11 = 61 + -28x + 3x2

Solving
-2.11 = 61 + -28x + 3x2

Solving for variable 'x'.

Combine like terms: -2.11 + -61 = -63.11
-63.11 + 28x + -3x2 = 61 + -28x + 3x2 + -61 + 28x + -3x2

Reorder the terms:
-63.11 + 28x + -3x2 = 61 + -61 + -28x + 28x + 3x2 + -3x2

Combine like terms: 61 + -61 = 0
-63.11 + 28x + -3x2 = 0 + -28x + 28x + 3x2 + -3x2
-63.11 + 28x + -3x2 = -28x + 28x + 3x2 + -3x2

Combine like terms: -28x + 28x = 0
-63.11 + 28x + -3x2 = 0 + 3x2 + -3x2
-63.11 + 28x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-63.11 + 28x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
21.03666667 + -9.333333333x + x2 = 0

Move the constant term to the right:

Add '-21.03666667' to each side of the equation.
21.03666667 + -9.333333333x + -21.03666667 + x2 = 0 + -21.03666667

Reorder the terms:
21.03666667 + -21.03666667 + -9.333333333x + x2 = 0 + -21.03666667

Combine like terms: 21.03666667 + -21.03666667 = 0.00000000
0.00000000 + -9.333333333x + x2 = 0 + -21.03666667
-9.333333333x + x2 = 0 + -21.03666667

Combine like terms: 0 + -21.03666667 = -21.03666667
-9.333333333x + x2 = -21.03666667

The x term is -9.333333333x.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333x + 21.77777778 + x2 = -21.03666667 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333x + x2 = -21.03666667 + 21.77777778

Combine like terms: -21.03666667 + 21.77777778 = 0.74111111
21.77777778 + -9.333333333x + x2 = 0.74111111

Factor a perfect square on the left side:
(x + -4.666666667)(x + -4.666666667) = 0.74111111

Calculate the square root of the right side: 0.860878104

Break this problem into two subproblems by setting 
(x + -4.666666667) equal to 0.860878104 and -0.860878104.


Subproblem 1
x + -4.666666667 = 0.860878104

Simplifying
x + -4.666666667 = 0.860878104

Reorder the terms:
-4.666666667 + x = 0.860878104

Solving
-4.666666667 + x = 0.860878104

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = 0.860878104 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = 0.860878104 + 4.666666667
x = 0.860878104 + 4.666666667

Combine like terms: 0.860878104 + 4.666666667 = 5.527544771
x = 5.527544771

Simplifying
x = 5.527544771


Subproblem 2
x + -4.666666667 = -0.860878104

Simplifying
x + -4.666666667 = -0.860878104

Reorder the terms:
-4.666666667 + x = -0.860878104

Solving
-4.666666667 + x = -0.860878104

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = -0.860878104 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = -0.860878104 + 4.666666667
x = -0.860878104 + 4.666666667

Combine like terms: -0.860878104 + 4.666666667 = 3.805788563
x = 3.805788563

Simplifying
x = 3.805788563


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.527544771, 3.805788563}

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