x^2+1.4x-18=0

Solution for x^2+1.4x-18=0 equation:

Simplifying
x2 + 1.4x + -18 = 0

Reorder the terms:
-18 + 1.4x + x2 = 0

Solving
-18 + 1.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 1.4x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + 1.4x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 1.4x + x2 = 0 + 18
1.4x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
1.4x + x2 = 18

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 = 18 + 0.49

Reorder the terms:
0.49 + 1.4x + x2 = 18 + 0.49

Combine like terms: 18 + 0.49 = 18.49
0.49 + 1.4x + x2 = 18.49

Factor a perfect square on the left side:
(x + 0.7)(x + 0.7) = 18.49

Calculate the square root of the right side: 4.3

Break this problem into two subproblems by setting 
(x + 0.7) equal to 4.3 and -4.3.

Subproblem 1
x + 0.7 = 4.3

Simplifying
x + 0.7 = 4.3

Reorder the terms:
0.7 + x = 4.3

Solving
0.7 + x = 4.3

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 = 4.3 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = 4.3 + -0.7
x = 4.3 + -0.7

Combine like terms: 4.3 + -0.7 = 3.6
x = 3.6

Simplifying
x = 3.6

Subproblem 2
x + 0.7 = -4.3

Simplifying
x + 0.7 = -4.3

Reorder the terms:
0.7 + x = -4.3

Solving
0.7 + x = -4.3

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 = -4.3 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + x = -4.3 + -0.7
x = -4.3 + -0.7

Combine like terms: -4.3 + -0.7 = -5
x = -5

Simplifying
x = -5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.6, -5}