1026.5=59.5x+x^2

Solution for 1026.5=59.5x+x^2 equation:

Simplifying
1026.5 = 59.5x + x2

Solving
1026.5 = 59.5x + x2

Solving for variable 'x'.

Reorder the terms:
1026.5 + -59.5x + -1x2 = 59.5x + -59.5x + x2 + -1x2

Combine like terms: 59.5x + -59.5x = 0.0
1026.5 + -59.5x + -1x2 = 0.0 + x2 + -1x2
1026.5 + -59.5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
1026.5 + -59.5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-1026.5 + 59.5x + x2 = 0

Move the constant term to the right:

Add '1026.5' to each side of the equation.
-1026.5 + 59.5x + 1026.5 + x2 = 0 + 1026.5

Reorder the terms:
-1026.5 + 1026.5 + 59.5x + x2 = 0 + 1026.5

Combine like terms: -1026.5 + 1026.5 = 0.0
0.0 + 59.5x + x2 = 0 + 1026.5
59.5x + x2 = 0 + 1026.5

Combine like terms: 0 + 1026.5 = 1026.5
59.5x + x2 = 1026.5

The x term is 59.5x.  Take half its coefficient (29.75).
Square it (885.0625) and add it to both sides.

Add '885.0625' to each side of the equation.
59.5x + 885.0625 + x2 = 1026.5 + 885.0625

Reorder the terms:
885.0625 + 59.5x + x2 = 1026.5 + 885.0625

Combine like terms: 1026.5 + 885.0625 = 1911.5625
885.0625 + 59.5x + x2 = 1911.5625

Factor a perfect square on the left side:
(x + 29.75)(x + 29.75) = 1911.5625

Calculate the square root of the right side: 43.721419236

Break this problem into two subproblems by setting 
(x + 29.75) equal to 43.721419236 and -43.721419236.

Subproblem 1
x + 29.75 = 43.721419236

Simplifying
x + 29.75 = 43.721419236

Reorder the terms:
29.75 + x = 43.721419236

Solving
29.75 + x = 43.721419236

Solving for variable 'x'.

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

Add '-29.75' to each side of the equation.
29.75 + -29.75 + x = 43.721419236 + -29.75

Combine like terms: 29.75 + -29.75 = 0.00
0.00 + x = 43.721419236 + -29.75
x = 43.721419236 + -29.75

Combine like terms: 43.721419236 + -29.75 = 13.971419236
x = 13.971419236

Simplifying
x = 13.971419236

Subproblem 2
x + 29.75 = -43.721419236

Simplifying
x + 29.75 = -43.721419236

Reorder the terms:
29.75 + x = -43.721419236

Solving
29.75 + x = -43.721419236

Solving for variable 'x'.

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

Add '-29.75' to each side of the equation.
29.75 + -29.75 + x = -43.721419236 + -29.75

Combine like terms: 29.75 + -29.75 = 0.00
0.00 + x = -43.721419236 + -29.75
x = -43.721419236 + -29.75

Combine like terms: -43.721419236 + -29.75 = -73.471419236
x = -73.471419236

Simplifying
x = -73.471419236

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.971419236, -73.471419236}