x^2-36+3.5x=0

Solution for x^2-36+3.5x=0 equation:

Simplifying
x2 + -36 + 3.5x = 0

Reorder the terms:
-36 + 3.5x + x2 = 0

Solving
-36 + 3.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 3.5x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 3.5x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 3.5x + x2 = 0 + 36
3.5x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
3.5x + x2 = 36

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 36 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 36 + 3.0625

Combine like terms: 36 + 3.0625 = 39.0625
3.0625 + 3.5x + x2 = 39.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 39.0625

Calculate the square root of the right side: 6.25

Break this problem into two subproblems by setting 
(x + 1.75) equal to 6.25 and -6.25.

Subproblem 1
x + 1.75 = 6.25

Simplifying
x + 1.75 = 6.25

Reorder the terms:
1.75 + x = 6.25

Solving
1.75 + x = 6.25

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 6.25 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 6.25 + -1.75
x = 6.25 + -1.75

Combine like terms: 6.25 + -1.75 = 4.5
x = 4.5

Simplifying
x = 4.5

Subproblem 2
x + 1.75 = -6.25

Simplifying
x + 1.75 = -6.25

Reorder the terms:
1.75 + x = -6.25

Solving
1.75 + x = -6.25

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -6.25 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -6.25 + -1.75
x = -6.25 + -1.75

Combine like terms: -6.25 + -1.75 = -8
x = -8

Simplifying
x = -8

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.5, -8}