(0.30-x)(0.40-x)=3.46

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Solution for (0.30-x)(0.40-x)=3.46 equation: 


Simplifying
(0.30 + -1x)(0.40 + -1x) = 3.46

Multiply (0.30 + -1x) * (0.40 + -1x)
(0.30(0.40 + -1x) + -1x * (0.40 + -1x)) = 3.46
((0.40 * 0.30 + -1x * 0.30) + -1x * (0.40 + -1x)) = 3.46
((0.12 + -0.3x) + -1x * (0.40 + -1x)) = 3.46
(0.12 + -0.3x + (0.40 * -1x + -1x * -1x)) = 3.46
(0.12 + -0.3x + (-0.4x + 1x2)) = 3.46

Combine like terms: -0.3x + -0.4x = -0.7x
(0.12 + -0.7x + 1x2) = 3.46

Solving
0.12 + -0.7x + 1x2 = 3.46

Solving for variable 'x'.

Reorder the terms:
0.12 + -3.46 + -0.7x + 1x2 = 3.46 + -3.46

Combine like terms: 0.12 + -3.46 = -3.34
-3.34 + -0.7x + 1x2 = 3.46 + -3.46

Combine like terms: 3.46 + -3.46 = 0.00
-3.34 + -0.7x + 1x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '3.34' to each side of the equation.
-3.34 + -0.7x + 3.34 + x2 = 0.00 + 3.34

Reorder the terms:
-3.34 + 3.34 + -0.7x + x2 = 0.00 + 3.34

Combine like terms: -3.34 + 3.34 = 0.00
0.00 + -0.7x + x2 = 0.00 + 3.34
-0.7x + x2 = 0.00 + 3.34

Combine like terms: 0.00 + 3.34 = 3.34
-0.7x + x2 = 3.34

The x term is -0.7x.  Take half its coefficient (-0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
-0.7x + 0.1225 + x2 = 3.34 + 0.1225

Reorder the terms:
0.1225 + -0.7x + x2 = 3.34 + 0.1225

Combine like terms: 3.34 + 0.1225 = 3.4625
0.1225 + -0.7x + x2 = 3.4625

Factor a perfect square on the left side:
(x + -0.35)(x + -0.35) = 3.4625

Calculate the square root of the right side: 1.860779407

Break this problem into two subproblems by setting 
(x + -0.35) equal to 1.860779407 and -1.860779407.


Subproblem 1
x + -0.35 = 1.860779407

Simplifying
x + -0.35 = 1.860779407

Reorder the terms:
-0.35 + x = 1.860779407

Solving
-0.35 + x = 1.860779407

Solving for variable 'x'.

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

Add '0.35' to each side of the equation.
-0.35 + 0.35 + x = 1.860779407 + 0.35

Combine like terms: -0.35 + 0.35 = 0.00
0.00 + x = 1.860779407 + 0.35
x = 1.860779407 + 0.35

Combine like terms: 1.860779407 + 0.35 = 2.210779407
x = 2.210779407

Simplifying
x = 2.210779407


Subproblem 2
x + -0.35 = -1.860779407

Simplifying
x + -0.35 = -1.860779407

Reorder the terms:
-0.35 + x = -1.860779407

Solving
-0.35 + x = -1.860779407

Solving for variable 'x'.

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

Add '0.35' to each side of the equation.
-0.35 + 0.35 + x = -1.860779407 + 0.35

Combine like terms: -0.35 + 0.35 = 0.00
0.00 + x = -1.860779407 + 0.35
x = -1.860779407 + 0.35

Combine like terms: -1.860779407 + 0.35 = -1.510779407
x = -1.510779407

Simplifying
x = -1.510779407


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.210779407, -1.510779407}

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