x(1.4+x)=2.6

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Solution for x(1.4+x)=2.6 equation: 


Simplifying
x(1.4 + x) = 2.6
(1.4 * x + x * x) = 2.6
(1.4x + x2) = 2.6

Solving
1.4x + x2 = 2.6

Solving for variable 'x'.

Reorder the terms:
-2.6 + 1.4x + x2 = 2.6 + -2.6

Combine like terms: 2.6 + -2.6 = 0.0
-2.6 + 1.4x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '2.6' to each side of the equation.
-2.6 + 1.4x + 2.6 + x2 = 0.0 + 2.6

Reorder the terms:
-2.6 + 2.6 + 1.4x + x2 = 0.0 + 2.6

Combine like terms: -2.6 + 2.6 = 0.0
0.0 + 1.4x + x2 = 0.0 + 2.6
1.4x + x2 = 0.0 + 2.6

Combine like terms: 0.0 + 2.6 = 2.6
1.4x + x2 = 2.6

The x term is 1.4x.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4x + 0.49 + x2 = 2.6 + 0.49

Reorder the terms:
0.49 + 1.4x + x2 = 2.6 + 0.49

Combine like terms: 2.6 + 0.49 = 3.09
0.49 + 1.4x + x2 = 3.09

Factor a perfect square on the left side:
(x + 0.7)(x + 0.7) = 3.09

Calculate the square root of the right side: 1.757839583

Break this problem into two subproblems by setting 
(x + 0.7) equal to 1.757839583 and -1.757839583.


Subproblem 1
x + 0.7 = 1.757839583

Simplifying
x + 0.7 = 1.757839583

Reorder the terms:
0.7 + x = 1.757839583

Solving
0.7 + x = 1.757839583

Solving for variable 'x'.

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

Add '-0.7' to each side of the equation.
0.7 + -0.7 + x = 1.757839583 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = 1.757839583 + -0.7
x = 1.757839583 + -0.7

Combine like terms: 1.757839583 + -0.7 = 1.057839583
x = 1.057839583

Simplifying
x = 1.057839583


Subproblem 2
x + 0.7 = -1.757839583

Simplifying
x + 0.7 = -1.757839583

Reorder the terms:
0.7 + x = -1.757839583

Solving
0.7 + x = -1.757839583

Solving for variable 'x'.

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

Add '-0.7' to each side of the equation.
0.7 + -0.7 + x = -1.757839583 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = -1.757839583 + -0.7
x = -1.757839583 + -0.7

Combine like terms: -1.757839583 + -0.7 = -2.457839583
x = -2.457839583

Simplifying
x = -2.457839583


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.057839583, -2.457839583}

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