x^2-4.7x+2.7=0

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Solution for x^2-4.7x+2.7=0 equation: 


Simplifying
x2 + -4.7x + 2.7 = 0

Reorder the terms:
2.7 + -4.7x + x2 = 0

Solving
2.7 + -4.7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.7' to each side of the equation.
2.7 + -4.7x + -2.7 + x2 = 0 + -2.7

Reorder the terms:
2.7 + -2.7 + -4.7x + x2 = 0 + -2.7

Combine like terms: 2.7 + -2.7 = 0.0
0.0 + -4.7x + x2 = 0 + -2.7
-4.7x + x2 = 0 + -2.7

Combine like terms: 0 + -2.7 = -2.7
-4.7x + x2 = -2.7

The x term is -4.7x.  Take half its coefficient (-2.35).
Square it (5.5225) and add it to both sides.

Add '5.5225' to each side of the equation.
-4.7x + 5.5225 + x2 = -2.7 + 5.5225

Reorder the terms:
5.5225 + -4.7x + x2 = -2.7 + 5.5225

Combine like terms: -2.7 + 5.5225 = 2.8225
5.5225 + -4.7x + x2 = 2.8225

Factor a perfect square on the left side:
(x + -2.35)(x + -2.35) = 2.8225

Calculate the square root of the right side: 1.680029762

Break this problem into two subproblems by setting 
(x + -2.35) equal to 1.680029762 and -1.680029762.


Subproblem 1
x + -2.35 = 1.680029762

Simplifying
x + -2.35 = 1.680029762

Reorder the terms:
-2.35 + x = 1.680029762

Solving
-2.35 + x = 1.680029762

Solving for variable 'x'.

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

Add '2.35' to each side of the equation.
-2.35 + 2.35 + x = 1.680029762 + 2.35

Combine like terms: -2.35 + 2.35 = 0.00
0.00 + x = 1.680029762 + 2.35
x = 1.680029762 + 2.35

Combine like terms: 1.680029762 + 2.35 = 4.030029762
x = 4.030029762

Simplifying
x = 4.030029762


Subproblem 2
x + -2.35 = -1.680029762

Simplifying
x + -2.35 = -1.680029762

Reorder the terms:
-2.35 + x = -1.680029762

Solving
-2.35 + x = -1.680029762

Solving for variable 'x'.

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

Add '2.35' to each side of the equation.
-2.35 + 2.35 + x = -1.680029762 + 2.35

Combine like terms: -2.35 + 2.35 = 0.00
0.00 + x = -1.680029762 + 2.35
x = -1.680029762 + 2.35

Combine like terms: -1.680029762 + 2.35 = 0.669970238
x = 0.669970238

Simplifying
x = 0.669970238


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.030029762, 0.669970238}

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