(x+0.9)(x+2.6)=0

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Solution for (x+0.9)(x+2.6)=0 equation:


Simplifying
(x + 0.9)(x + 2.6) = 0

Reorder the terms:
(0.9 + x)(x + 2.6) = 0

Reorder the terms:
(0.9 + x)(2.6 + x) = 0

Multiply (0.9 + x) * (2.6 + x)
(0.9(2.6 + x) + x(2.6 + x)) = 0
((2.6 * 0.9 + x * 0.9) + x(2.6 + x)) = 0
((2.34 + 0.9x) + x(2.6 + x)) = 0
(2.34 + 0.9x + (2.6 * x + x * x)) = 0
(2.34 + 0.9x + (2.6x + x2)) = 0

Combine like terms: 0.9x + 2.6x = 3.5x
(2.34 + 3.5x + x2) = 0

Solving
2.34 + 3.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2.34' to each side of the equation.
2.34 + 3.5x + -2.34 + x2 = 0 + -2.34

Reorder the terms:
2.34 + -2.34 + 3.5x + x2 = 0 + -2.34

Combine like terms: 2.34 + -2.34 = 0.00
0.00 + 3.5x + x2 = 0 + -2.34
3.5x + x2 = 0 + -2.34

Combine like terms: 0 + -2.34 = -2.34
3.5x + x2 = -2.34

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 = -2.34 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = -2.34 + 3.0625

Combine like terms: -2.34 + 3.0625 = 0.7225
3.0625 + 3.5x + x2 = 0.7225

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 0.7225

Calculate the square root of the right side: 0.85

Break this problem into two subproblems by setting 
(x + 1.75) equal to 0.85 and -0.85.


Subproblem 1
x + 1.75 = 0.85

Simplifying
x + 1.75 = 0.85

Reorder the terms:
1.75 + x = 0.85

Solving
1.75 + x = 0.85

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 = 0.85 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 0.85 + -1.75
x = 0.85 + -1.75

Combine like terms: 0.85 + -1.75 = -0.9
x = -0.9

Simplifying
x = -0.9


Subproblem 2
x + 1.75 = -0.85

Simplifying
x + 1.75 = -0.85

Reorder the terms:
1.75 + x = -0.85

Solving
1.75 + x = -0.85

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 = -0.85 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -0.85 + -1.75
x = -0.85 + -1.75

Combine like terms: -0.85 + -1.75 = -2.6
x = -2.6

Simplifying
x = -2.6


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.9, -2.6}

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