10x^2-6x-64=0

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Solution for 10x^2-6x-64=0 equation: 


Simplifying
10x2 + -6x + -64 = 0

Reorder the terms:
-64 + -6x + 10x2 = 0

Solving
-64 + -6x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-32 + -3x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-32 + -3x + 5x2)' equal to zero and attempt to solve:

Simplifying
-32 + -3x + 5x2 = 0

Solving
-32 + -3x + 5x2 = 0

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

Divide each side by '5'.
-6.4 + -0.6x + x2 = 0

Move the constant term to the right:

Add '6.4' to each side of the equation.
-6.4 + -0.6x + 6.4 + x2 = 0 + 6.4

Reorder the terms:
-6.4 + 6.4 + -0.6x + x2 = 0 + 6.4

Combine like terms: -6.4 + 6.4 = 0.0
0.0 + -0.6x + x2 = 0 + 6.4
-0.6x + x2 = 0 + 6.4

Combine like terms: 0 + 6.4 = 6.4
-0.6x + x2 = 6.4

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 = 6.4 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 6.4 + 0.09

Combine like terms: 6.4 + 0.09 = 6.49
0.09 + -0.6x + x2 = 6.49

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 6.49

Calculate the square root of the right side: 2.547547841

Break this problem into two subproblems by setting 
(x + -0.3) equal to 2.547547841 and -2.547547841.


Subproblem 1
x + -0.3 = 2.547547841

Simplifying
x + -0.3 = 2.547547841

Reorder the terms:
-0.3 + x = 2.547547841

Solving
-0.3 + x = 2.547547841

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 = 2.547547841 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = 2.547547841 + 0.3
x = 2.547547841 + 0.3

Combine like terms: 2.547547841 + 0.3 = 2.847547841
x = 2.847547841

Simplifying
x = 2.847547841


Subproblem 2
x + -0.3 = -2.547547841

Simplifying
x + -0.3 = -2.547547841

Reorder the terms:
-0.3 + x = -2.547547841

Solving
-0.3 + x = -2.547547841

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 = -2.547547841 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + x = -2.547547841 + 0.3
x = -2.547547841 + 0.3

Combine like terms: -2.547547841 + 0.3 = -2.247547841
x = -2.247547841

Simplifying
x = -2.247547841


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.847547841, -2.247547841}
Solution
x = {2.847547841, -2.247547841}

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