x^2+45x-567=0

Solution for x^2+45x-567=0 equation:

Simplifying
x2 + 45x + -567 = 0

Reorder the terms:
-567 + 45x + x2 = 0

Solving
-567 + 45x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '567' to each side of the equation.
-567 + 45x + 567 + x2 = 0 + 567

Reorder the terms:
-567 + 567 + 45x + x2 = 0 + 567

Combine like terms: -567 + 567 = 0
0 + 45x + x2 = 0 + 567
45x + x2 = 0 + 567

Combine like terms: 0 + 567 = 567
45x + x2 = 567

The x term is 45x.  Take half its coefficient (22.5).
Square it (506.25) and add it to both sides.

Add '506.25' to each side of the equation.
45x + 506.25 + x2 = 567 + 506.25

Reorder the terms:
506.25 + 45x + x2 = 567 + 506.25

Combine like terms: 567 + 506.25 = 1073.25
506.25 + 45x + x2 = 1073.25

Factor a perfect square on the left side:
(x + 22.5)(x + 22.5) = 1073.25

Calculate the square root of the right side: 32.760494502

Break this problem into two subproblems by setting 
(x + 22.5) equal to 32.760494502 and -32.760494502.

Subproblem 1
x + 22.5 = 32.760494502

Simplifying
x + 22.5 = 32.760494502

Reorder the terms:
22.5 + x = 32.760494502

Solving
22.5 + x = 32.760494502

Solving for variable 'x'.

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

Add '-22.5' to each side of the equation.
22.5 + -22.5 + x = 32.760494502 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + x = 32.760494502 + -22.5
x = 32.760494502 + -22.5

Combine like terms: 32.760494502 + -22.5 = 10.260494502
x = 10.260494502

Simplifying
x = 10.260494502

Subproblem 2
x + 22.5 = -32.760494502

Simplifying
x + 22.5 = -32.760494502

Reorder the terms:
22.5 + x = -32.760494502

Solving
22.5 + x = -32.760494502

Solving for variable 'x'.

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

Add '-22.5' to each side of the equation.
22.5 + -22.5 + x = -32.760494502 + -22.5

Combine like terms: 22.5 + -22.5 = 0.0
0.0 + x = -32.760494502 + -22.5
x = -32.760494502 + -22.5

Combine like terms: -32.760494502 + -22.5 = -55.260494502
x = -55.260494502

Simplifying
x = -55.260494502

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.260494502, -55.260494502}