(x+0.4)(x+7)=0

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Solution for (x+0.4)(x+7)=0 equation: 


Simplifying
(x + 0.4)(x + 7) = 0

Reorder the terms:
(0.4 + x)(x + 7) = 0

Reorder the terms:
(0.4 + x)(7 + x) = 0

Multiply (0.4 + x) * (7 + x)
(0.4(7 + x) + x(7 + x)) = 0
((7 * 0.4 + x * 0.4) + x(7 + x)) = 0
((2.8 + 0.4x) + x(7 + x)) = 0
(2.8 + 0.4x + (7 * x + x * x)) = 0
(2.8 + 0.4x + (7x + x2)) = 0

Combine like terms: 0.4x + 7x = 7.4x
(2.8 + 7.4x + x2) = 0

Solving
2.8 + 7.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.8' to each side of the equation.
2.8 + 7.4x + -2.8 + x2 = 0 + -2.8

Reorder the terms:
2.8 + -2.8 + 7.4x + x2 = 0 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + 7.4x + x2 = 0 + -2.8
7.4x + x2 = 0 + -2.8

Combine like terms: 0 + -2.8 = -2.8
7.4x + x2 = -2.8

The x term is 7.4x.  Take half its coefficient (3.7).
Square it (13.69) and add it to both sides.

Add '13.69' to each side of the equation.
7.4x + 13.69 + x2 = -2.8 + 13.69

Reorder the terms:
13.69 + 7.4x + x2 = -2.8 + 13.69

Combine like terms: -2.8 + 13.69 = 10.89
13.69 + 7.4x + x2 = 10.89

Factor a perfect square on the left side:
(x + 3.7)(x + 3.7) = 10.89

Calculate the square root of the right side: 3.3

Break this problem into two subproblems by setting 
(x + 3.7) equal to 3.3 and -3.3.


Subproblem 1
x + 3.7 = 3.3

Simplifying
x + 3.7 = 3.3

Reorder the terms:
3.7 + x = 3.3

Solving
3.7 + x = 3.3

Solving for variable 'x'.

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

Add '-3.7' to each side of the equation.
3.7 + -3.7 + x = 3.3 + -3.7

Combine like terms: 3.7 + -3.7 = 0.0
0.0 + x = 3.3 + -3.7
x = 3.3 + -3.7

Combine like terms: 3.3 + -3.7 = -0.4
x = -0.4

Simplifying
x = -0.4


Subproblem 2
x + 3.7 = -3.3

Simplifying
x + 3.7 = -3.3

Reorder the terms:
3.7 + x = -3.3

Solving
3.7 + x = -3.3

Solving for variable 'x'.

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

Add '-3.7' to each side of the equation.
3.7 + -3.7 + x = -3.3 + -3.7

Combine like terms: 3.7 + -3.7 = 0.0
0.0 + x = -3.3 + -3.7
x = -3.3 + -3.7

Combine like terms: -3.3 + -3.7 = -7
x = -7

Simplifying
x = -7


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.4, -7}

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