3x^2-4.7x+0.4=0

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Solution for 3x^2-4.7x+0.4=0 equation: 


Simplifying
3x2 + -4.7x + 0.4 = 0

Reorder the terms:
0.4 + -4.7x + 3x2 = 0

Solving
0.4 + -4.7x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
0.1333333333 + -1.566666667x + x2 = 0

Move the constant term to the right:

Add '-0.1333333333' to each side of the equation.
0.1333333333 + -1.566666667x + -0.1333333333 + x2 = 0 + -0.1333333333

Reorder the terms:
0.1333333333 + -0.1333333333 + -1.566666667x + x2 = 0 + -0.1333333333

Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000
0.0000000000 + -1.566666667x + x2 = 0 + -0.1333333333
-1.566666667x + x2 = 0 + -0.1333333333

Combine like terms: 0 + -0.1333333333 = -0.1333333333
-1.566666667x + x2 = -0.1333333333

The x term is -1.566666667x.  Take half its coefficient (-0.7833333335).
Square it (0.6136111114) and add it to both sides.

Add '0.6136111114' to each side of the equation.
-1.566666667x + 0.6136111114 + x2 = -0.1333333333 + 0.6136111114

Reorder the terms:
0.6136111114 + -1.566666667x + x2 = -0.1333333333 + 0.6136111114

Combine like terms: -0.1333333333 + 0.6136111114 = 0.4802777781
0.6136111114 + -1.566666667x + x2 = 0.4802777781

Factor a perfect square on the left side:
(x + -0.7833333335)(x + -0.7833333335) = 0.4802777781

Calculate the square root of the right side: 0.693020763

Break this problem into two subproblems by setting 
(x + -0.7833333335) equal to 0.693020763 and -0.693020763.


Subproblem 1
x + -0.7833333335 = 0.693020763

Simplifying
x + -0.7833333335 = 0.693020763

Reorder the terms:
-0.7833333335 + x = 0.693020763

Solving
-0.7833333335 + x = 0.693020763

Solving for variable 'x'.

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

Add '0.7833333335' to each side of the equation.
-0.7833333335 + 0.7833333335 + x = 0.693020763 + 0.7833333335

Combine like terms: -0.7833333335 + 0.7833333335 = 0.0000000000
0.0000000000 + x = 0.693020763 + 0.7833333335
x = 0.693020763 + 0.7833333335

Combine like terms: 0.693020763 + 0.7833333335 = 1.4763540965
x = 1.4763540965

Simplifying
x = 1.4763540965


Subproblem 2
x + -0.7833333335 = -0.693020763

Simplifying
x + -0.7833333335 = -0.693020763

Reorder the terms:
-0.7833333335 + x = -0.693020763

Solving
-0.7833333335 + x = -0.693020763

Solving for variable 'x'.

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

Add '0.7833333335' to each side of the equation.
-0.7833333335 + 0.7833333335 + x = -0.693020763 + 0.7833333335

Combine like terms: -0.7833333335 + 0.7833333335 = 0.0000000000
0.0000000000 + x = -0.693020763 + 0.7833333335
x = -0.693020763 + 0.7833333335

Combine like terms: -0.693020763 + 0.7833333335 = 0.0903125705
x = 0.0903125705

Simplifying
x = 0.0903125705


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4763540965, 0.0903125705}

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