7x^2+6x-529=0

Solution for 7x^2+6x-529=0 equation:

Simplifying
7x2 + 6x + -529 = 0

Reorder the terms:
-529 + 6x + 7x2 = 0

Solving
-529 + 6x + 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'.
-75.57142857 + 0.8571428571x + x2 = 0

Move the constant term to the right:

Add '75.57142857' to each side of the equation.
-75.57142857 + 0.8571428571x + 75.57142857 + x2 = 0 + 75.57142857

Reorder the terms:
-75.57142857 + 75.57142857 + 0.8571428571x + x2 = 0 + 75.57142857

Combine like terms: -75.57142857 + 75.57142857 = 0.00000000
0.00000000 + 0.8571428571x + x2 = 0 + 75.57142857
0.8571428571x + x2 = 0 + 75.57142857

Combine like terms: 0 + 75.57142857 = 75.57142857
0.8571428571x + x2 = 75.57142857

The x term is 0.8571428571x.  Take half its coefficient (0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
0.8571428571x + 0.1836734694 + x2 = 75.57142857 + 0.1836734694

Reorder the terms:
0.1836734694 + 0.8571428571x + x2 = 75.57142857 + 0.1836734694

Combine like terms: 75.57142857 + 0.1836734694 = 75.7551020394
0.1836734694 + 0.8571428571x + x2 = 75.7551020394

Factor a perfect square on the left side:
(x + 0.4285714286)(x + 0.4285714286) = 75.7551020394

Calculate the square root of the right side: 8.703740692

Break this problem into two subproblems by setting 
(x + 0.4285714286) equal to 8.703740692 and -8.703740692.

Subproblem 1
x + 0.4285714286 = 8.703740692

Simplifying
x + 0.4285714286 = 8.703740692

Reorder the terms:
0.4285714286 + x = 8.703740692

Solving
0.4285714286 + x = 8.703740692

Solving for variable 'x'.

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

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -0.4285714286 + x = 8.703740692 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + x = 8.703740692 + -0.4285714286
x = 8.703740692 + -0.4285714286

Combine like terms: 8.703740692 + -0.4285714286 = 8.2751692634
x = 8.2751692634

Simplifying
x = 8.2751692634

Subproblem 2
x + 0.4285714286 = -8.703740692

Simplifying
x + 0.4285714286 = -8.703740692

Reorder the terms:
0.4285714286 + x = -8.703740692

Solving
0.4285714286 + x = -8.703740692

Solving for variable 'x'.

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

Add '-0.4285714286' to each side of the equation.
0.4285714286 + -0.4285714286 + x = -8.703740692 + -0.4285714286

Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000
0.0000000000 + x = -8.703740692 + -0.4285714286
x = -8.703740692 + -0.4285714286

Combine like terms: -8.703740692 + -0.4285714286 = -9.1323121206
x = -9.1323121206

Simplifying
x = -9.1323121206

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.2751692634, -9.1323121206}