7x*x+8x-1=0

Solution for 7x*x+8x-1=0 equation:

Simplifying
7x * x + 8x + -1 = 0

Multiply x * x
7x2 + 8x + -1 = 0

Reorder the terms:
-1 + 8x + 7x2 = 0

Solving
-1 + 8x + 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'.
-0.1428571429 + 1.142857143x + x2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 1.142857143x + 0.1428571429 + x2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + 1.142857143x + x2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + 1.142857143x + x2 = 0 + 0.1428571429
1.142857143x + x2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
1.142857143x + x2 = 0.1428571429

The x term is 1.142857143x.  Take half its coefficient (0.5714285715).
Square it (0.3265306123) and add it to both sides.

Add '0.3265306123' to each side of the equation.
1.142857143x + 0.3265306123 + x2 = 0.1428571429 + 0.3265306123

Reorder the terms:
0.3265306123 + 1.142857143x + x2 = 0.1428571429 + 0.3265306123

Combine like terms: 0.1428571429 + 0.3265306123 = 0.4693877552
0.3265306123 + 1.142857143x + x2 = 0.4693877552

Factor a perfect square on the left side:
(x + 0.5714285715)(x + 0.5714285715) = 0.4693877552

Calculate the square root of the right side: 0.685118789

Break this problem into two subproblems by setting 
(x + 0.5714285715) equal to 0.685118789 and -0.685118789.

Subproblem 1
x + 0.5714285715 = 0.685118789

Simplifying
x + 0.5714285715 = 0.685118789

Reorder the terms:
0.5714285715 + x = 0.685118789

Solving
0.5714285715 + x = 0.685118789

Solving for variable 'x'.

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

Add '-0.5714285715' to each side of the equation.
0.5714285715 + -0.5714285715 + x = 0.685118789 + -0.5714285715

Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000
0.0000000000 + x = 0.685118789 + -0.5714285715
x = 0.685118789 + -0.5714285715

Combine like terms: 0.685118789 + -0.5714285715 = 0.1136902175
x = 0.1136902175

Simplifying
x = 0.1136902175

Subproblem 2
x + 0.5714285715 = -0.685118789

Simplifying
x + 0.5714285715 = -0.685118789

Reorder the terms:
0.5714285715 + x = -0.685118789

Solving
0.5714285715 + x = -0.685118789

Solving for variable 'x'.

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

Add '-0.5714285715' to each side of the equation.
0.5714285715 + -0.5714285715 + x = -0.685118789 + -0.5714285715

Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000
0.0000000000 + x = -0.685118789 + -0.5714285715
x = -0.685118789 + -0.5714285715

Combine like terms: -0.685118789 + -0.5714285715 = -1.2565473605
x = -1.2565473605

Simplifying
x = -1.2565473605

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.1136902175, -1.2565473605}