7x^2+18x-5=0

Solution for 7x^2+18x-5=0 equation:

Simplifying
7x2 + 18x + -5 = 0

Reorder the terms:
-5 + 18x + 7x2 = 0

Solving
-5 + 18x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-0.7142857143 + 2.571428571x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + 2.571428571x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + 2.571428571x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + 2.571428571x + x2 = 0 + 0.7142857143
2.571428571x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
2.571428571x + x2 = 0.7142857143

The x term is 2.571428571x.  Take half its coefficient (1.285714286).
Square it (1.653061225) and add it to both sides.

Add '1.653061225' to each side of the equation.
2.571428571x + 1.653061225 + x2 = 0.7142857143 + 1.653061225

Reorder the terms:
1.653061225 + 2.571428571x + x2 = 0.7142857143 + 1.653061225

Combine like terms: 0.7142857143 + 1.653061225 = 2.3673469393
1.653061225 + 2.571428571x + x2 = 2.3673469393

Factor a perfect square on the left side:
(x + 1.285714286)(x + 1.285714286) = 2.3673469393

Calculate the square root of the right side: 1.538618516

Break this problem into two subproblems by setting 
(x + 1.285714286) equal to 1.538618516 and -1.538618516.

Subproblem 1
x + 1.285714286 = 1.538618516

Simplifying
x + 1.285714286 = 1.538618516

Reorder the terms:
1.285714286 + x = 1.538618516

Solving
1.285714286 + x = 1.538618516

Solving for variable 'x'.

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

Add '-1.285714286' to each side of the equation.
1.285714286 + -1.285714286 + x = 1.538618516 + -1.285714286

Combine like terms: 1.285714286 + -1.285714286 = 0.000000000
0.000000000 + x = 1.538618516 + -1.285714286
x = 1.538618516 + -1.285714286

Combine like terms: 1.538618516 + -1.285714286 = 0.25290423
x = 0.25290423

Simplifying
x = 0.25290423

Subproblem 2
x + 1.285714286 = -1.538618516

Simplifying
x + 1.285714286 = -1.538618516

Reorder the terms:
1.285714286 + x = -1.538618516

Solving
1.285714286 + x = -1.538618516

Solving for variable 'x'.

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

Add '-1.285714286' to each side of the equation.
1.285714286 + -1.285714286 + x = -1.538618516 + -1.285714286

Combine like terms: 1.285714286 + -1.285714286 = 0.000000000
0.000000000 + x = -1.538618516 + -1.285714286
x = -1.538618516 + -1.285714286

Combine like terms: -1.538618516 + -1.285714286 = -2.824332802
x = -2.824332802

Simplifying
x = -2.824332802

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.25290423, -2.824332802}