16x^6+36x^4+49x^5=

Solution for 16x^6+36x^4+49x^5= equation:

Simplifying
16x6 + 36x4 + 49x5 = 0

Reorder the terms:
36x4 + 49x5 + 16x6 = 0

Solving
36x4 + 49x5 + 16x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x4'.
x4(36 + 49x + 16x2) = 0

Subproblem 1
Set the factor 'x4' equal to zero and attempt to solve:

Simplifying
x4 = 0

Solving
x4 = 0

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

Simplifying
x4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(36 + 49x + 16x2)' equal to zero and attempt to solve:

Simplifying
36 + 49x + 16x2 = 0

Solving
36 + 49x + 16x2 = 0

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

Divide each side by '16'.
2.25 + 3.0625x + x2 = 0

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + 3.0625x + -2.25 + x2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + 3.0625x + x2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + 3.0625x + x2 = 0 + -2.25
3.0625x + x2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
3.0625x + x2 = -2.25

The x term is 3.0625x.  Take half its coefficient (1.53125).
Square it (2.344726563) and add it to both sides.

Add '2.344726563' to each side of the equation.
3.0625x + 2.344726563 + x2 = -2.25 + 2.344726563

Reorder the terms:
2.344726563 + 3.0625x + x2 = -2.25 + 2.344726563

Combine like terms: -2.25 + 2.344726563 = 0.094726563
2.344726563 + 3.0625x + x2 = 0.094726563

Factor a perfect square on the left side:
(x + 1.53125)(x + 1.53125) = 0.094726563

Calculate the square root of the right side: 0.307776807

Break this problem into two subproblems by setting 
(x + 1.53125) equal to 0.307776807 and -0.307776807.

Subproblem 1
x + 1.53125 = 0.307776807

Simplifying
x + 1.53125 = 0.307776807

Reorder the terms:
1.53125 + x = 0.307776807

Solving
1.53125 + x = 0.307776807

Solving for variable 'x'.

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

Add '-1.53125' to each side of the equation.
1.53125 + -1.53125 + x = 0.307776807 + -1.53125

Combine like terms: 1.53125 + -1.53125 = 0.00000
0.00000 + x = 0.307776807 + -1.53125
x = 0.307776807 + -1.53125

Combine like terms: 0.307776807 + -1.53125 = -1.223473193
x = -1.223473193

Simplifying
x = -1.223473193

Subproblem 2
x + 1.53125 = -0.307776807

Simplifying
x + 1.53125 = -0.307776807

Reorder the terms:
1.53125 + x = -0.307776807

Solving
1.53125 + x = -0.307776807

Solving for variable 'x'.

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

Add '-1.53125' to each side of the equation.
1.53125 + -1.53125 + x = -0.307776807 + -1.53125

Combine like terms: 1.53125 + -1.53125 = 0.00000
0.00000 + x = -0.307776807 + -1.53125
x = -0.307776807 + -1.53125

Combine like terms: -0.307776807 + -1.53125 = -1.839026807
x = -1.839026807

Simplifying
x = -1.839026807

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.223473193, -1.839026807}
Solution
x = {-1.223473193, -1.839026807}