13.95=x(x+1.4)

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Solution for 13.95=x(x+1.4) equation: 


Simplifying
13.95 = x(x + 1.4)

Reorder the terms:
13.95 = x(1.4 + x)
13.95 = (1.4 * x + x * x)
13.95 = (1.4x + x2)

Solving
13.95 = 1.4x + x2

Solving for variable 'x'.

Reorder the terms:
13.95 + -1.4x + -1x2 = 1.4x + -1.4x + x2 + -1x2

Combine like terms: 1.4x + -1.4x = 0.0
13.95 + -1.4x + -1x2 = 0.0 + x2 + -1x2
13.95 + -1.4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
13.95 + -1.4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-13.95 + 1.4x + x2 = 0

Move the constant term to the right:

Add '13.95' to each side of the equation.
-13.95 + 1.4x + 13.95 + x2 = 0 + 13.95

Reorder the terms:
-13.95 + 13.95 + 1.4x + x2 = 0 + 13.95

Combine like terms: -13.95 + 13.95 = 0.00
0.00 + 1.4x + x2 = 0 + 13.95
1.4x + x2 = 0 + 13.95

Combine like terms: 0 + 13.95 = 13.95
1.4x + x2 = 13.95

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 = 13.95 + 0.49

Reorder the terms:
0.49 + 1.4x + x2 = 13.95 + 0.49

Combine like terms: 13.95 + 0.49 = 14.44
0.49 + 1.4x + x2 = 14.44

Factor a perfect square on the left side:
(x + 0.7)(x + 0.7) = 14.44

Calculate the square root of the right side: 3.8

Break this problem into two subproblems by setting 
(x + 0.7) equal to 3.8 and -3.8.


Subproblem 1
x + 0.7 = 3.8

Simplifying
x + 0.7 = 3.8

Reorder the terms:
0.7 + x = 3.8

Solving
0.7 + x = 3.8

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 = 3.8 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = 3.8 + -0.7
x = 3.8 + -0.7

Combine like terms: 3.8 + -0.7 = 3.1
x = 3.1

Simplifying
x = 3.1


Subproblem 2
x + 0.7 = -3.8

Simplifying
x + 0.7 = -3.8

Reorder the terms:
0.7 + x = -3.8

Solving
0.7 + x = -3.8

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 = -3.8 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = -3.8 + -0.7
x = -3.8 + -0.7

Combine like terms: -3.8 + -0.7 = -4.5
x = -4.5

Simplifying
x = -4.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.1, -4.5}

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