7x^2-9x-26=0

Solution for 7x^2-9x-26=0 equation:

Simplifying
7x2 + -9x + -26 = 0

Reorder the terms:
-26 + -9x + 7x2 = 0

Solving
-26 + -9x + 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'.
-3.714285714 + -1.285714286x + x2 = 0

Move the constant term to the right:

Add '3.714285714' to each side of the equation.
-3.714285714 + -1.285714286x + 3.714285714 + x2 = 0 + 3.714285714

Reorder the terms:
-3.714285714 + 3.714285714 + -1.285714286x + x2 = 0 + 3.714285714

Combine like terms: -3.714285714 + 3.714285714 = 0.000000000
0.000000000 + -1.285714286x + x2 = 0 + 3.714285714
-1.285714286x + x2 = 0 + 3.714285714

Combine like terms: 0 + 3.714285714 = 3.714285714
-1.285714286x + x2 = 3.714285714

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 = 3.714285714 + 0.4132653063

Reorder the terms:
0.4132653063 + -1.285714286x + x2 = 3.714285714 + 0.4132653063

Combine like terms: 3.714285714 + 0.4132653063 = 4.1275510203
0.4132653063 + -1.285714286x + x2 = 4.1275510203

Factor a perfect square on the left side:
(x + -0.642857143)(x + -0.642857143) = 4.1275510203

Calculate the square root of the right side: 2.031637522

Break this problem into two subproblems by setting 
(x + -0.642857143) equal to 2.031637522 and -2.031637522.

Subproblem 1
x + -0.642857143 = 2.031637522

Simplifying
x + -0.642857143 = 2.031637522

Reorder the terms:
-0.642857143 + x = 2.031637522

Solving
-0.642857143 + x = 2.031637522

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 = 2.031637522 + 0.642857143

Combine like terms: -0.642857143 + 0.642857143 = 0.000000000
0.000000000 + x = 2.031637522 + 0.642857143
x = 2.031637522 + 0.642857143

Combine like terms: 2.031637522 + 0.642857143 = 2.674494665
x = 2.674494665

Simplifying
x = 2.674494665

Subproblem 2
x + -0.642857143 = -2.031637522

Simplifying
x + -0.642857143 = -2.031637522

Reorder the terms:
-0.642857143 + x = -2.031637522

Solving
-0.642857143 + x = -2.031637522

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 = -2.031637522 + 0.642857143

Combine like terms: -0.642857143 + 0.642857143 = 0.000000000
0.000000000 + x = -2.031637522 + 0.642857143
x = -2.031637522 + 0.642857143

Combine like terms: -2.031637522 + 0.642857143 = -1.388780379
x = -1.388780379

Simplifying
x = -1.388780379

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.674494665, -1.388780379}