(5x^2-2x-64)+(4x^2+8x)=

Solution for (5x^2-2x-64)+(4x^2+8x)= equation:

Simplifying
(5x2 + -2x + -64) + (4x2 + 8x) = 0

Reorder the terms:
(-64 + -2x + 5x2) + (4x2 + 8x) = 0

Remove parenthesis around (-64 + -2x + 5x2)
-64 + -2x + 5x2 + (4x2 + 8x) = 0

Reorder the terms:
-64 + -2x + 5x2 + (8x + 4x2) = 0

Remove parenthesis around (8x + 4x2)
-64 + -2x + 5x2 + 8x + 4x2 = 0

Reorder the terms:
-64 + -2x + 8x + 5x2 + 4x2 = 0

Combine like terms: -2x + 8x = 6x
-64 + 6x + 5x2 + 4x2 = 0

Combine like terms: 5x2 + 4x2 = 9x2
-64 + 6x + 9x2 = 0

Solving
-64 + 6x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-7.111111111 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '7.111111111' to each side of the equation.
-7.111111111 + 0.6666666667x + 7.111111111 + x2 = 0 + 7.111111111

Reorder the terms:
-7.111111111 + 7.111111111 + 0.6666666667x + x2 = 0 + 7.111111111

Combine like terms: -7.111111111 + 7.111111111 = 0.000000000
0.000000000 + 0.6666666667x + x2 = 0 + 7.111111111
0.6666666667x + x2 = 0 + 7.111111111

Combine like terms: 0 + 7.111111111 = 7.111111111
0.6666666667x + x2 = 7.111111111

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 7.111111111 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 7.111111111 + 0.1111111112

Combine like terms: 7.111111111 + 0.1111111112 = 7.2222222222
0.1111111112 + 0.6666666667x + x2 = 7.2222222222

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 7.2222222222

Calculate the square root of the right side: 2.687419249

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 2.687419249 and -2.687419249.

Subproblem 1
x + 0.3333333334 = 2.687419249

Simplifying
x + 0.3333333334 = 2.687419249

Reorder the terms:
0.3333333334 + x = 2.687419249

Solving
0.3333333334 + x = 2.687419249

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 2.687419249 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 2.687419249 + -0.3333333334
x = 2.687419249 + -0.3333333334

Combine like terms: 2.687419249 + -0.3333333334 = 2.3540859156
x = 2.3540859156

Simplifying
x = 2.3540859156

Subproblem 2
x + 0.3333333334 = -2.687419249

Simplifying
x + 0.3333333334 = -2.687419249

Reorder the terms:
0.3333333334 + x = -2.687419249

Solving
0.3333333334 + x = -2.687419249

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -2.687419249 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -2.687419249 + -0.3333333334
x = -2.687419249 + -0.3333333334

Combine like terms: -2.687419249 + -0.3333333334 = -3.0207525824
x = -3.0207525824

Simplifying
x = -3.0207525824

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.3540859156, -3.0207525824}