x^2+56x-406.25=0

Solution for x^2+56x-406.25=0 equation:

Simplifying
x2 + 56x + -406.25 = 0

Reorder the terms:
-406.25 + 56x + x2 = 0

Solving
-406.25 + 56x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '406.25' to each side of the equation.
-406.25 + 56x + 406.25 + x2 = 0 + 406.25

Reorder the terms:
-406.25 + 406.25 + 56x + x2 = 0 + 406.25

Combine like terms: -406.25 + 406.25 = 0.00
0.00 + 56x + x2 = 0 + 406.25
56x + x2 = 0 + 406.25

Combine like terms: 0 + 406.25 = 406.25
56x + x2 = 406.25

The x term is 56x.  Take half its coefficient (28).
Square it (784) and add it to both sides.

Add '784' to each side of the equation.
56x + 784 + x2 = 406.25 + 784

Reorder the terms:
784 + 56x + x2 = 406.25 + 784

Combine like terms: 406.25 + 784 = 1190.25
784 + 56x + x2 = 1190.25

Factor a perfect square on the left side:
(x + 28)(x + 28) = 1190.25

Calculate the square root of the right side: 34.5

Break this problem into two subproblems by setting 
(x + 28) equal to 34.5 and -34.5.

Subproblem 1
x + 28 = 34.5

Simplifying
x + 28 = 34.5

Reorder the terms:
28 + x = 34.5

Solving
28 + x = 34.5

Solving for variable 'x'.

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

Add '-28' to each side of the equation.
28 + -28 + x = 34.5 + -28

Combine like terms: 28 + -28 = 0
0 + x = 34.5 + -28
x = 34.5 + -28

Combine like terms: 34.5 + -28 = 6.5
x = 6.5

Simplifying
x = 6.5

Subproblem 2
x + 28 = -34.5

Simplifying
x + 28 = -34.5

Reorder the terms:
28 + x = -34.5

Solving
28 + x = -34.5

Solving for variable 'x'.

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

Add '-28' to each side of the equation.
28 + -28 + x = -34.5 + -28

Combine like terms: 28 + -28 = 0
0 + x = -34.5 + -28
x = -34.5 + -28

Combine like terms: -34.5 + -28 = -62.5
x = -62.5

Simplifying
x = -62.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.5, -62.5}