-7x^2-4x+13=0

Solution for -7x^2-4x+13=0 equation:

Simplifying
-7x2 + -4x + 13 = 0

Reorder the terms:
13 + -4x + -7x2 = 0

Solving
13 + -4x + -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'.
-1.857142857 + 0.5714285714x + x2 = 0

Move the constant term to the right:

Add '1.857142857' to each side of the equation.
-1.857142857 + 0.5714285714x + 1.857142857 + x2 = 0 + 1.857142857

Reorder the terms:
-1.857142857 + 1.857142857 + 0.5714285714x + x2 = 0 + 1.857142857

Combine like terms: -1.857142857 + 1.857142857 = 0.000000000
0.000000000 + 0.5714285714x + x2 = 0 + 1.857142857
0.5714285714x + x2 = 0 + 1.857142857

Combine like terms: 0 + 1.857142857 = 1.857142857
0.5714285714x + x2 = 1.857142857

The x term is 0.5714285714x.  Take half its coefficient (0.2857142857).
Square it (0.08163265305) and add it to both sides.

Add '0.08163265305' to each side of the equation.
0.5714285714x + 0.08163265305 + x2 = 1.857142857 + 0.08163265305

Reorder the terms:
0.08163265305 + 0.5714285714x + x2 = 1.857142857 + 0.08163265305

Combine like terms: 1.857142857 + 0.08163265305 = 1.93877551005
0.08163265305 + 0.5714285714x + x2 = 1.93877551005

Factor a perfect square on the left side:
(x + 0.2857142857)(x + 0.2857142857) = 1.93877551005

Calculate the square root of the right side: 1.392399192

Break this problem into two subproblems by setting 
(x + 0.2857142857) equal to 1.392399192 and -1.392399192.

Subproblem 1
x + 0.2857142857 = 1.392399192

Simplifying
x + 0.2857142857 = 1.392399192

Reorder the terms:
0.2857142857 + x = 1.392399192

Solving
0.2857142857 + x = 1.392399192

Solving for variable 'x'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + x = 1.392399192 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = 1.392399192 + -0.2857142857
x = 1.392399192 + -0.2857142857

Combine like terms: 1.392399192 + -0.2857142857 = 1.1066849063
x = 1.1066849063

Simplifying
x = 1.1066849063

Subproblem 2
x + 0.2857142857 = -1.392399192

Simplifying
x + 0.2857142857 = -1.392399192

Reorder the terms:
0.2857142857 + x = -1.392399192

Solving
0.2857142857 + x = -1.392399192

Solving for variable 'x'.

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

Add '-0.2857142857' to each side of the equation.
0.2857142857 + -0.2857142857 + x = -1.392399192 + -0.2857142857

Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000
0.0000000000 + x = -1.392399192 + -0.2857142857
x = -1.392399192 + -0.2857142857

Combine like terms: -1.392399192 + -0.2857142857 = -1.6781134777
x = -1.6781134777

Simplifying
x = -1.6781134777

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1066849063, -1.6781134777}