(x+0.5)(x+1.4)=0

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Solution for (x+0.5)(x+1.4)=0 equation: 


Simplifying
(x + 0.5)(x + 1.4) = 0

Reorder the terms:
(0.5 + x)(x + 1.4) = 0

Reorder the terms:
(0.5 + x)(1.4 + x) = 0

Multiply (0.5 + x) * (1.4 + x)
(0.5(1.4 + x) + x(1.4 + x)) = 0
((1.4 * 0.5 + x * 0.5) + x(1.4 + x)) = 0
((0.7 + 0.5x) + x(1.4 + x)) = 0
(0.7 + 0.5x + (1.4 * x + x * x)) = 0
(0.7 + 0.5x + (1.4x + x2)) = 0

Combine like terms: 0.5x + 1.4x = 1.9x
(0.7 + 1.9x + x2) = 0

Solving
0.7 + 1.9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.7' to each side of the equation.
0.7 + 1.9x + -0.7 + x2 = 0 + -0.7

Reorder the terms:
0.7 + -0.7 + 1.9x + x2 = 0 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + 1.9x + x2 = 0 + -0.7
1.9x + x2 = 0 + -0.7

Combine like terms: 0 + -0.7 = -0.7
1.9x + x2 = -0.7

The x term is 1.9x.  Take half its coefficient (0.95).
Square it (0.9025) and add it to both sides.

Add '0.9025' to each side of the equation.
1.9x + 0.9025 + x2 = -0.7 + 0.9025

Reorder the terms:
0.9025 + 1.9x + x2 = -0.7 + 0.9025

Combine like terms: -0.7 + 0.9025 = 0.2025
0.9025 + 1.9x + x2 = 0.2025

Factor a perfect square on the left side:
(x + 0.95)(x + 0.95) = 0.2025

Calculate the square root of the right side: 0.45

Break this problem into two subproblems by setting 
(x + 0.95) equal to 0.45 and -0.45.


Subproblem 1
x + 0.95 = 0.45

Simplifying
x + 0.95 = 0.45

Reorder the terms:
0.95 + x = 0.45

Solving
0.95 + x = 0.45

Solving for variable 'x'.

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

Add '-0.95' to each side of the equation.
0.95 + -0.95 + x = 0.45 + -0.95

Combine like terms: 0.95 + -0.95 = 0.00
0.00 + x = 0.45 + -0.95
x = 0.45 + -0.95

Combine like terms: 0.45 + -0.95 = -0.5
x = -0.5

Simplifying
x = -0.5


Subproblem 2
x + 0.95 = -0.45

Simplifying
x + 0.95 = -0.45

Reorder the terms:
0.95 + x = -0.45

Solving
0.95 + x = -0.45

Solving for variable 'x'.

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

Add '-0.95' to each side of the equation.
0.95 + -0.95 + x = -0.45 + -0.95

Combine like terms: 0.95 + -0.95 = 0.00
0.00 + x = -0.45 + -0.95
x = -0.45 + -0.95

Combine like terms: -0.45 + -0.95 = -1.4
x = -1.4

Simplifying
x = -1.4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5, -1.4}

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