14x^2+18x-21=0

Solution for 14x^2+18x-21=0 equation:

Simplifying
14x2 + 18x + -21 = 0

Reorder the terms:
-21 + 18x + 14x2 = 0

Solving
-21 + 18x + 14x2 = 0

Solving for variable 'x'.

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

Divide each side by '14'.
-1.5 + 1.285714286x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 1.285714286x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 1.285714286x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 1.285714286x + x2 = 0 + 1.5
1.285714286x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
1.285714286x + x2 = 1.5

The x term is 1.285714286x.  Take half its coefficient (0.642857143).
Square it (0.4132653063) and add it to both sides.

Add '0.4132653063' to each side of the equation.
1.285714286x + 0.4132653063 + x2 = 1.5 + 0.4132653063

Reorder the terms:
0.4132653063 + 1.285714286x + x2 = 1.5 + 0.4132653063

Combine like terms: 1.5 + 0.4132653063 = 1.9132653063
0.4132653063 + 1.285714286x + x2 = 1.9132653063

Factor a perfect square on the left side:
(x + 0.642857143)(x + 0.642857143) = 1.9132653063

Calculate the square root of the right side: 1.383208338

Break this problem into two subproblems by setting 
(x + 0.642857143) equal to 1.383208338 and -1.383208338.

Subproblem 1
x + 0.642857143 = 1.383208338

Simplifying
x + 0.642857143 = 1.383208338

Reorder the terms:
0.642857143 + x = 1.383208338

Solving
0.642857143 + x = 1.383208338

Solving for variable 'x'.

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

Add '-0.642857143' to each side of the equation.
0.642857143 + -0.642857143 + x = 1.383208338 + -0.642857143

Combine like terms: 0.642857143 + -0.642857143 = 0.000000000
0.000000000 + x = 1.383208338 + -0.642857143
x = 1.383208338 + -0.642857143

Combine like terms: 1.383208338 + -0.642857143 = 0.740351195
x = 0.740351195

Simplifying
x = 0.740351195

Subproblem 2
x + 0.642857143 = -1.383208338

Simplifying
x + 0.642857143 = -1.383208338

Reorder the terms:
0.642857143 + x = -1.383208338

Solving
0.642857143 + x = -1.383208338

Solving for variable 'x'.

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

Add '-0.642857143' to each side of the equation.
0.642857143 + -0.642857143 + x = -1.383208338 + -0.642857143

Combine like terms: 0.642857143 + -0.642857143 = 0.000000000
0.000000000 + x = -1.383208338 + -0.642857143
x = -1.383208338 + -0.642857143

Combine like terms: -1.383208338 + -0.642857143 = -2.026065481
x = -2.026065481

Simplifying
x = -2.026065481

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.740351195, -2.026065481}