(3x^2-7x-44)+(8x^2+9x)=

Solution for (3x^2-7x-44)+(8x^2+9x)= equation:

Simplifying
(3x2 + -7x + -44) + (8x2 + 9x) = 0

Reorder the terms:
(-44 + -7x + 3x2) + (8x2 + 9x) = 0

Remove parenthesis around (-44 + -7x + 3x2)
-44 + -7x + 3x2 + (8x2 + 9x) = 0

Reorder the terms:
-44 + -7x + 3x2 + (9x + 8x2) = 0

Remove parenthesis around (9x + 8x2)
-44 + -7x + 3x2 + 9x + 8x2 = 0

Reorder the terms:
-44 + -7x + 9x + 3x2 + 8x2 = 0

Combine like terms: -7x + 9x = 2x
-44 + 2x + 3x2 + 8x2 = 0

Combine like terms: 3x2 + 8x2 = 11x2
-44 + 2x + 11x2 = 0

Solving
-44 + 2x + 11x2 = 0

Solving for variable 'x'.

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

Divide each side by '11'.
-4 + 0.1818181818x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 0.1818181818x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + 0.1818181818x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 0.1818181818x + x2 = 0 + 4
0.1818181818x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
0.1818181818x + x2 = 4

The x term is 0.1818181818x.  Take half its coefficient (0.0909090909).
Square it (0.008264462808) and add it to both sides.

Add '0.008264462808' to each side of the equation.
0.1818181818x + 0.008264462808 + x2 = 4 + 0.008264462808

Reorder the terms:
0.008264462808 + 0.1818181818x + x2 = 4 + 0.008264462808

Combine like terms: 4 + 0.008264462808 = 4.008264462808
0.008264462808 + 0.1818181818x + x2 = 4.008264462808

Factor a perfect square on the left side:
(x + 0.0909090909)(x + 0.0909090909) = 4.008264462808

Calculate the square root of the right side: 2.00206505

Break this problem into two subproblems by setting 
(x + 0.0909090909) equal to 2.00206505 and -2.00206505.

Subproblem 1
x + 0.0909090909 = 2.00206505

Simplifying
x + 0.0909090909 = 2.00206505

Reorder the terms:
0.0909090909 + x = 2.00206505

Solving
0.0909090909 + x = 2.00206505

Solving for variable 'x'.

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

Add '-0.0909090909' to each side of the equation.
0.0909090909 + -0.0909090909 + x = 2.00206505 + -0.0909090909

Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000
0.0000000000 + x = 2.00206505 + -0.0909090909
x = 2.00206505 + -0.0909090909

Combine like terms: 2.00206505 + -0.0909090909 = 1.9111559591
x = 1.9111559591

Simplifying
x = 1.9111559591

Subproblem 2
x + 0.0909090909 = -2.00206505

Simplifying
x + 0.0909090909 = -2.00206505

Reorder the terms:
0.0909090909 + x = -2.00206505

Solving
0.0909090909 + x = -2.00206505

Solving for variable 'x'.

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

Add '-0.0909090909' to each side of the equation.
0.0909090909 + -0.0909090909 + x = -2.00206505 + -0.0909090909

Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000
0.0000000000 + x = -2.00206505 + -0.0909090909
x = -2.00206505 + -0.0909090909

Combine like terms: -2.00206505 + -0.0909090909 = -2.0929741409
x = -2.0929741409

Simplifying
x = -2.0929741409

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.9111559591, -2.0929741409}