x^2+1.4x=1.2

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Solution for x^2+1.4x=1.2 equation: 


Simplifying
x2 + 1.4x = 1.2

Reorder the terms:
1.4x + x2 = 1.2

Solving
1.4x + x2 = 1.2

Solving for variable 'x'.

Reorder the terms:
-1.2 + 1.4x + x2 = 1.2 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
-1.2 + 1.4x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + 1.4x + 1.2 + x2 = 0.0 + 1.2

Reorder the terms:
-1.2 + 1.2 + 1.4x + x2 = 0.0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + 1.4x + x2 = 0.0 + 1.2
1.4x + x2 = 0.0 + 1.2

Combine like terms: 0.0 + 1.2 = 1.2
1.4x + x2 = 1.2

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 = 1.2 + 0.49

Reorder the terms:
0.49 + 1.4x + x2 = 1.2 + 0.49

Combine like terms: 1.2 + 0.49 = 1.69
0.49 + 1.4x + x2 = 1.69

Factor a perfect square on the left side:
(x + 0.7)(x + 0.7) = 1.69

Calculate the square root of the right side: 1.3

Break this problem into two subproblems by setting 
(x + 0.7) equal to 1.3 and -1.3.


Subproblem 1
x + 0.7 = 1.3

Simplifying
x + 0.7 = 1.3

Reorder the terms:
0.7 + x = 1.3

Solving
0.7 + x = 1.3

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 = 1.3 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = 1.3 + -0.7
x = 1.3 + -0.7

Combine like terms: 1.3 + -0.7 = 0.6
x = 0.6

Simplifying
x = 0.6


Subproblem 2
x + 0.7 = -1.3

Simplifying
x + 0.7 = -1.3

Reorder the terms:
0.7 + x = -1.3

Solving
0.7 + x = -1.3

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 = -1.3 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = -1.3 + -0.7
x = -1.3 + -0.7

Combine like terms: -1.3 + -0.7 = -2
x = -2

Simplifying
x = -2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6, -2}

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