-40=-2.096x^2-2.25x+9.038

Solution for -40=-2.096x^2-2.25x+9.038 equation:

Simplifying
-40 = -2.096x2 + -2.25x + 9.038

Reorder the terms:
-40 = 9.038 + -2.25x + -2.096x2

Solving
-40 = 9.038 + -2.25x + -2.096x2

Solving for variable 'x'.

Combine like terms: -40 + -9.038 = -49.038
-49.038 + 2.25x + 2.096x2 = 9.038 + -2.25x + -2.096x2 + -9.038 + 2.25x + 2.096x2

Reorder the terms:
-49.038 + 2.25x + 2.096x2 = 9.038 + -9.038 + -2.25x + 2.25x + -2.096x2 + 2.096x2

Combine like terms: 9.038 + -9.038 = 0.000
-49.038 + 2.25x + 2.096x2 = 0.000 + -2.25x + 2.25x + -2.096x2 + 2.096x2
-49.038 + 2.25x + 2.096x2 = -2.25x + 2.25x + -2.096x2 + 2.096x2

Combine like terms: -2.25x + 2.25x = 0.00
-49.038 + 2.25x + 2.096x2 = 0.00 + -2.096x2 + 2.096x2
-49.038 + 2.25x + 2.096x2 = -2.096x2 + 2.096x2

Combine like terms: -2.096x2 + 2.096x2 = 0.000
-49.038 + 2.25x + 2.096x2 = 0.000

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

Divide each side by '2.096'.
-23.39599237 + 1.073473282x + x2 = 0

Move the constant term to the right:

Add '23.39599237' to each side of the equation.
-23.39599237 + 1.073473282x + 23.39599237 + x2 = 0 + 23.39599237

Reorder the terms:
-23.39599237 + 23.39599237 + 1.073473282x + x2 = 0 + 23.39599237

Combine like terms: -23.39599237 + 23.39599237 = 0.00000000
0.00000000 + 1.073473282x + x2 = 0 + 23.39599237
1.073473282x + x2 = 0 + 23.39599237

Combine like terms: 0 + 23.39599237 = 23.39599237
1.073473282x + x2 = 23.39599237

The x term is 1.073473282x.  Take half its coefficient (0.536736641).
Square it (0.2880862218) and add it to both sides.

Add '0.2880862218' to each side of the equation.
1.073473282x + 0.2880862218 + x2 = 23.39599237 + 0.2880862218

Reorder the terms:
0.2880862218 + 1.073473282x + x2 = 23.39599237 + 0.2880862218

Combine like terms: 23.39599237 + 0.2880862218 = 23.6840785918
0.2880862218 + 1.073473282x + x2 = 23.6840785918

Factor a perfect square on the left side:
(x + 0.536736641)(x + 0.536736641) = 23.6840785918

Calculate the square root of the right side: 4.866629079

Break this problem into two subproblems by setting 
(x + 0.536736641) equal to 4.866629079 and -4.866629079.

Subproblem 1
x + 0.536736641 = 4.866629079

Simplifying
x + 0.536736641 = 4.866629079

Reorder the terms:
0.536736641 + x = 4.866629079

Solving
0.536736641 + x = 4.866629079

Solving for variable 'x'.

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

Add '-0.536736641' to each side of the equation.
0.536736641 + -0.536736641 + x = 4.866629079 + -0.536736641

Combine like terms: 0.536736641 + -0.536736641 = 0.000000000
0.000000000 + x = 4.866629079 + -0.536736641
x = 4.866629079 + -0.536736641

Combine like terms: 4.866629079 + -0.536736641 = 4.329892438
x = 4.329892438

Simplifying
x = 4.329892438

Subproblem 2
x + 0.536736641 = -4.866629079

Simplifying
x + 0.536736641 = -4.866629079

Reorder the terms:
0.536736641 + x = -4.866629079

Solving
0.536736641 + x = -4.866629079

Solving for variable 'x'.

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

Add '-0.536736641' to each side of the equation.
0.536736641 + -0.536736641 + x = -4.866629079 + -0.536736641

Combine like terms: 0.536736641 + -0.536736641 = 0.000000000
0.000000000 + x = -4.866629079 + -0.536736641
x = -4.866629079 + -0.536736641

Combine like terms: -4.866629079 + -0.536736641 = -5.40336572
x = -5.40336572

Simplifying
x = -5.40336572

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.329892438, -5.40336572}