10x^2-64=36+6x

Solution for 10x^2-64=36+6x equation:

Simplifying
10x2 + -64 = 36 + 6x

Reorder the terms:
-64 + 10x2 = 36 + 6x

Solving
-64 + 10x2 = 36 + 6x

Solving for variable 'x'.

Reorder the terms:
-64 + -36 + -6x + 10x2 = 36 + 6x + -36 + -6x

Combine like terms: -64 + -36 = -100
-100 + -6x + 10x2 = 36 + 6x + -36 + -6x

Reorder the terms:
-100 + -6x + 10x2 = 36 + -36 + 6x + -6x

Combine like terms: 36 + -36 = 0
-100 + -6x + 10x2 = 0 + 6x + -6x
-100 + -6x + 10x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-100 + -6x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + -3x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-50 + -3x + 5x2)' equal to zero and attempt to solve:

Simplifying
-50 + -3x + 5x2 = 0

Solving
-50 + -3x + 5x2 = 0

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

Divide each side by '5'.
-10 + -0.6x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -0.6x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -0.6x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -0.6x + x2 = 0 + 10
-0.6x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-0.6x + x2 = 10

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 10 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 10 + 0.09

Combine like terms: 10 + 0.09 = 10.09
0.09 + -0.6x + x2 = 10.09

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 10.09

Calculate the square root of the right side: 3.176476035

Break this problem into two subproblems by setting 
(x + -0.3) equal to 3.176476035 and -3.176476035.

Subproblem 1
x + -0.3 = 3.176476035

Simplifying
x + -0.3 = 3.176476035

Reorder the terms:
-0.3 + x = 3.176476035

Solving
-0.3 + x = 3.176476035

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = 3.176476035 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = 3.176476035 + 0.3
x = 3.176476035 + 0.3

Combine like terms: 3.176476035 + 0.3 = 3.476476035
x = 3.476476035

Simplifying
x = 3.476476035

Subproblem 2
x + -0.3 = -3.176476035

Simplifying
x + -0.3 = -3.176476035

Reorder the terms:
-0.3 + x = -3.176476035

Solving
-0.3 + x = -3.176476035

Solving for variable 'x'.

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

Add '0.3' to each side of the equation.
-0.3 + 0.3 + x = -3.176476035 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = -3.176476035 + 0.3
x = -3.176476035 + 0.3

Combine like terms: -3.176476035 + 0.3 = -2.876476035
x = -2.876476035

Simplifying
x = -2.876476035

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.476476035, -2.876476035}
Solution
x = {3.476476035, -2.876476035}