9x^2+14x-4=0

Solution for 9x^2+14x-4=0 equation:

Simplifying
9x2 + 14x + -4 = 0

Reorder the terms:
-4 + 14x + 9x2 = 0

Solving
-4 + 14x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-0.4444444444 + 1.555555556x + x2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + 1.555555556x + 0.4444444444 + x2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + 1.555555556x + x2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + 1.555555556x + x2 = 0 + 0.4444444444
1.555555556x + x2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
1.555555556x + x2 = 0.4444444444

The x term is 1.555555556x.  Take half its coefficient (0.777777778).
Square it (0.6049382720) and add it to both sides.

Add '0.6049382720' to each side of the equation.
1.555555556x + 0.6049382720 + x2 = 0.4444444444 + 0.6049382720

Reorder the terms:
0.6049382720 + 1.555555556x + x2 = 0.4444444444 + 0.6049382720

Combine like terms: 0.4444444444 + 0.6049382720 = 1.0493827164
0.6049382720 + 1.555555556x + x2 = 1.0493827164

Factor a perfect square on the left side:
(x + 0.777777778)(x + 0.777777778) = 1.0493827164

Calculate the square root of the right side: 1.024393829

Break this problem into two subproblems by setting 
(x + 0.777777778) equal to 1.024393829 and -1.024393829.

Subproblem 1
x + 0.777777778 = 1.024393829

Simplifying
x + 0.777777778 = 1.024393829

Reorder the terms:
0.777777778 + x = 1.024393829

Solving
0.777777778 + x = 1.024393829

Solving for variable 'x'.

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

Add '-0.777777778' to each side of the equation.
0.777777778 + -0.777777778 + x = 1.024393829 + -0.777777778

Combine like terms: 0.777777778 + -0.777777778 = 0.000000000
0.000000000 + x = 1.024393829 + -0.777777778
x = 1.024393829 + -0.777777778

Combine like terms: 1.024393829 + -0.777777778 = 0.246616051
x = 0.246616051

Simplifying
x = 0.246616051

Subproblem 2
x + 0.777777778 = -1.024393829

Simplifying
x + 0.777777778 = -1.024393829

Reorder the terms:
0.777777778 + x = -1.024393829

Solving
0.777777778 + x = -1.024393829

Solving for variable 'x'.

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

Add '-0.777777778' to each side of the equation.
0.777777778 + -0.777777778 + x = -1.024393829 + -0.777777778

Combine like terms: 0.777777778 + -0.777777778 = 0.000000000
0.000000000 + x = -1.024393829 + -0.777777778
x = -1.024393829 + -0.777777778

Combine like terms: -1.024393829 + -0.777777778 = -1.802171607
x = -1.802171607

Simplifying
x = -1.802171607

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.246616051, -1.802171607}