x^2+9x-42.25=0

Solution for x^2+9x-42.25=0 equation:

Simplifying
x2 + 9x + -42.25 = 0

Reorder the terms:
-42.25 + 9x + x2 = 0

Solving
-42.25 + 9x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '42.25' to each side of the equation.
-42.25 + 9x + 42.25 + x2 = 0 + 42.25

Reorder the terms:
-42.25 + 42.25 + 9x + x2 = 0 + 42.25

Combine like terms: -42.25 + 42.25 = 0.00
0.00 + 9x + x2 = 0 + 42.25
9x + x2 = 0 + 42.25

Combine like terms: 0 + 42.25 = 42.25
9x + x2 = 42.25

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = 42.25 + 20.25

Reorder the terms:
20.25 + 9x + x2 = 42.25 + 20.25

Combine like terms: 42.25 + 20.25 = 62.5
20.25 + 9x + x2 = 62.5

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 62.5

Calculate the square root of the right side: 7.90569415

Break this problem into two subproblems by setting 
(x + 4.5) equal to 7.90569415 and -7.90569415.

Subproblem 1
x + 4.5 = 7.90569415

Simplifying
x + 4.5 = 7.90569415

Reorder the terms:
4.5 + x = 7.90569415

Solving
4.5 + x = 7.90569415

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = 7.90569415 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = 7.90569415 + -4.5
x = 7.90569415 + -4.5

Combine like terms: 7.90569415 + -4.5 = 3.40569415
x = 3.40569415

Simplifying
x = 3.40569415

Subproblem 2
x + 4.5 = -7.90569415

Simplifying
x + 4.5 = -7.90569415

Reorder the terms:
4.5 + x = -7.90569415

Solving
4.5 + x = -7.90569415

Solving for variable 'x'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + x = -7.90569415 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + x = -7.90569415 + -4.5
x = -7.90569415 + -4.5

Combine like terms: -7.90569415 + -4.5 = -12.40569415
x = -12.40569415

Simplifying
x = -12.40569415

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.40569415, -12.40569415}