x^2-4.3x+2.7=0

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Solution for x^2-4.3x+2.7=0 equation: 


Simplifying
x2 + -4.3x + 2.7 = 0

Reorder the terms:
2.7 + -4.3x + x2 = 0

Solving
2.7 + -4.3x + 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 + -4.3x + -2.7 + x2 = 0 + -2.7

Reorder the terms:
2.7 + -2.7 + -4.3x + x2 = 0 + -2.7

Combine like terms: 2.7 + -2.7 = 0.0
0.0 + -4.3x + x2 = 0 + -2.7
-4.3x + x2 = 0 + -2.7

Combine like terms: 0 + -2.7 = -2.7
-4.3x + x2 = -2.7

The x term is -4.3x.  Take half its coefficient (-2.15).
Square it (4.6225) and add it to both sides.

Add '4.6225' to each side of the equation.
-4.3x + 4.6225 + x2 = -2.7 + 4.6225

Reorder the terms:
4.6225 + -4.3x + x2 = -2.7 + 4.6225

Combine like terms: -2.7 + 4.6225 = 1.9225
4.6225 + -4.3x + x2 = 1.9225

Factor a perfect square on the left side:
(x + -2.15)(x + -2.15) = 1.9225

Calculate the square root of the right side: 1.386542462

Break this problem into two subproblems by setting 
(x + -2.15) equal to 1.386542462 and -1.386542462.


Subproblem 1
x + -2.15 = 1.386542462

Simplifying
x + -2.15 = 1.386542462

Reorder the terms:
-2.15 + x = 1.386542462

Solving
-2.15 + x = 1.386542462

Solving for variable 'x'.

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

Add '2.15' to each side of the equation.
-2.15 + 2.15 + x = 1.386542462 + 2.15

Combine like terms: -2.15 + 2.15 = 0.00
0.00 + x = 1.386542462 + 2.15
x = 1.386542462 + 2.15

Combine like terms: 1.386542462 + 2.15 = 3.536542462
x = 3.536542462

Simplifying
x = 3.536542462


Subproblem 2
x + -2.15 = -1.386542462

Simplifying
x + -2.15 = -1.386542462

Reorder the terms:
-2.15 + x = -1.386542462

Solving
-2.15 + x = -1.386542462

Solving for variable 'x'.

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

Add '2.15' to each side of the equation.
-2.15 + 2.15 + x = -1.386542462 + 2.15

Combine like terms: -2.15 + 2.15 = 0.00
0.00 + x = -1.386542462 + 2.15
x = -1.386542462 + 2.15

Combine like terms: -1.386542462 + 2.15 = 0.763457538
x = 0.763457538

Simplifying
x = 0.763457538


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.536542462, 0.763457538}

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