7x^2+282x-529=0

Solution for 7x^2+282x-529=0 equation:

Simplifying
7x2 + 282x + -529 = 0

Reorder the terms:
-529 + 282x + 7x2 = 0

Solving
-529 + 282x + 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 + 40.28571429x + x2 = 0

Move the constant term to the right:

Add '75.57142857' to each side of the equation.
-75.57142857 + 40.28571429x + 75.57142857 + x2 = 0 + 75.57142857

Reorder the terms:
-75.57142857 + 75.57142857 + 40.28571429x + x2 = 0 + 75.57142857

Combine like terms: -75.57142857 + 75.57142857 = 0.00000000
0.00000000 + 40.28571429x + x2 = 0 + 75.57142857
40.28571429x + x2 = 0 + 75.57142857

Combine like terms: 0 + 75.57142857 = 75.57142857
40.28571429x + x2 = 75.57142857

The x term is 40.28571429x.  Take half its coefficient (20.14285715).
Square it (405.7346942) and add it to both sides.

Add '405.7346942' to each side of the equation.
40.28571429x + 405.7346942 + x2 = 75.57142857 + 405.7346942

Reorder the terms:
405.7346942 + 40.28571429x + x2 = 75.57142857 + 405.7346942

Combine like terms: 75.57142857 + 405.7346942 = 481.30612277
405.7346942 + 40.28571429x + x2 = 481.30612277

Factor a perfect square on the left side:
(x + 20.14285715)(x + 20.14285715) = 481.30612277

Calculate the square root of the right side: 21.938690088

Break this problem into two subproblems by setting 
(x + 20.14285715) equal to 21.938690088 and -21.938690088.

Subproblem 1
x + 20.14285715 = 21.938690088

Simplifying
x + 20.14285715 = 21.938690088

Reorder the terms:
20.14285715 + x = 21.938690088

Solving
20.14285715 + x = 21.938690088

Solving for variable 'x'.

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

Add '-20.14285715' to each side of the equation.
20.14285715 + -20.14285715 + x = 21.938690088 + -20.14285715

Combine like terms: 20.14285715 + -20.14285715 = 0.00000000
0.00000000 + x = 21.938690088 + -20.14285715
x = 21.938690088 + -20.14285715

Combine like terms: 21.938690088 + -20.14285715 = 1.795832938
x = 1.795832938

Simplifying
x = 1.795832938

Subproblem 2
x + 20.14285715 = -21.938690088

Simplifying
x + 20.14285715 = -21.938690088

Reorder the terms:
20.14285715 + x = -21.938690088

Solving
20.14285715 + x = -21.938690088

Solving for variable 'x'.

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

Add '-20.14285715' to each side of the equation.
20.14285715 + -20.14285715 + x = -21.938690088 + -20.14285715

Combine like terms: 20.14285715 + -20.14285715 = 0.00000000
0.00000000 + x = -21.938690088 + -20.14285715
x = -21.938690088 + -20.14285715

Combine like terms: -21.938690088 + -20.14285715 = -42.081547238
x = -42.081547238

Simplifying
x = -42.081547238

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.795832938, -42.081547238}