0.4(7+2x)1.5x=3.4

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Solution for 0.4(7+2x)1.5x=3.4 equation: 


Simplifying
0.4(7 + 2x) * 1.5x = 3.4

Reorder the terms for easier multiplication:
0.4 * 1.5x(7 + 2x) = 3.4

Multiply 0.4 * 1.5
0.6x(7 + 2x) = 3.4
(7 * 0.6x + 2x * 0.6x) = 3.4
(4.2x + 1.2x2) = 3.4

Solving
4.2x + 1.2x2 = 3.4

Solving for variable 'x'.

Reorder the terms:
-3.4 + 4.2x + 1.2x2 = 3.4 + -3.4

Combine like terms: 3.4 + -3.4 = 0.0
-3.4 + 4.2x + 1.2x2 = 0.0

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

Divide each side by '1.2'.
-2.833333333 + 3.5x + x2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + 3.5x + 2.833333333 + x2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + 3.5x + x2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + 3.5x + x2 = 0 + 2.833333333
3.5x + x2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
3.5x + x2 = 2.833333333

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 2.833333333 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 2.833333333 + 3.0625

Combine like terms: 2.833333333 + 3.0625 = 5.895833333
3.0625 + 3.5x + x2 = 5.895833333

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 5.895833333

Calculate the square root of the right side: 2.428133714

Break this problem into two subproblems by setting 
(x + 1.75) equal to 2.428133714 and -2.428133714.


Subproblem 1
x + 1.75 = 2.428133714

Simplifying
x + 1.75 = 2.428133714

Reorder the terms:
1.75 + x = 2.428133714

Solving
1.75 + x = 2.428133714

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 2.428133714 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 2.428133714 + -1.75
x = 2.428133714 + -1.75

Combine like terms: 2.428133714 + -1.75 = 0.678133714
x = 0.678133714

Simplifying
x = 0.678133714


Subproblem 2
x + 1.75 = -2.428133714

Simplifying
x + 1.75 = -2.428133714

Reorder the terms:
1.75 + x = -2.428133714

Solving
1.75 + x = -2.428133714

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -2.428133714 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -2.428133714 + -1.75
x = -2.428133714 + -1.75

Combine like terms: -2.428133714 + -1.75 = -4.178133714
x = -4.178133714

Simplifying
x = -4.178133714


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.678133714, -4.178133714}

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