(3.4-x)(2.0-x)=0

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Solution for (3.4-x)(2.0-x)=0 equation: 


Simplifying
(3.4 + -1x)(2.0 + -1x) = 0

Multiply (3.4 + -1x) * (2.0 + -1x)
(3.4(2.0 + -1x) + -1x * (2.0 + -1x)) = 0
((2.0 * 3.4 + -1x * 3.4) + -1x * (2.0 + -1x)) = 0
((6.8 + -3.4x) + -1x * (2.0 + -1x)) = 0
(6.8 + -3.4x + (2.0 * -1x + -1x * -1x)) = 0
(6.8 + -3.4x + (-2x + 1x2)) = 0

Combine like terms: -3.4x + -2x = -5.4x
(6.8 + -5.4x + 1x2) = 0

Solving
6.8 + -5.4x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-6.8' to each side of the equation.
6.8 + -5.4x + -6.8 + x2 = 0 + -6.8

Reorder the terms:
6.8 + -6.8 + -5.4x + x2 = 0 + -6.8

Combine like terms: 6.8 + -6.8 = 0.0
0.0 + -5.4x + x2 = 0 + -6.8
-5.4x + x2 = 0 + -6.8

Combine like terms: 0 + -6.8 = -6.8
-5.4x + x2 = -6.8

The x term is -5.4x.  Take half its coefficient (-2.7).
Square it (7.29) and add it to both sides.

Add '7.29' to each side of the equation.
-5.4x + 7.29 + x2 = -6.8 + 7.29

Reorder the terms:
7.29 + -5.4x + x2 = -6.8 + 7.29

Combine like terms: -6.8 + 7.29 = 0.49
7.29 + -5.4x + x2 = 0.49

Factor a perfect square on the left side:
(x + -2.7)(x + -2.7) = 0.49

Calculate the square root of the right side: 0.7

Break this problem into two subproblems by setting 
(x + -2.7) equal to 0.7 and -0.7.


Subproblem 1
x + -2.7 = 0.7

Simplifying
x + -2.7 = 0.7

Reorder the terms:
-2.7 + x = 0.7

Solving
-2.7 + x = 0.7

Solving for variable 'x'.

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

Add '2.7' to each side of the equation.
-2.7 + 2.7 + x = 0.7 + 2.7

Combine like terms: -2.7 + 2.7 = 0.0
0.0 + x = 0.7 + 2.7
x = 0.7 + 2.7

Combine like terms: 0.7 + 2.7 = 3.4
x = 3.4

Simplifying
x = 3.4


Subproblem 2
x + -2.7 = -0.7

Simplifying
x + -2.7 = -0.7

Reorder the terms:
-2.7 + x = -0.7

Solving
-2.7 + x = -0.7

Solving for variable 'x'.

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

Add '2.7' to each side of the equation.
-2.7 + 2.7 + x = -0.7 + 2.7

Combine like terms: -2.7 + 2.7 = 0.0
0.0 + x = -0.7 + 2.7
x = -0.7 + 2.7

Combine like terms: -0.7 + 2.7 = 2
x = 2

Simplifying
x = 2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.4, 2}

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