100x^2-644x-64=0

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Solution for 100x^2-644x-64=0 equation: 


Simplifying
100x2 + -644x + -64 = 0

Reorder the terms:
-64 + -644x + 100x2 = 0

Solving
-64 + -644x + 100x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + -161x + 25x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-16 + -161x + 25x2)' equal to zero and attempt to solve:

Simplifying
-16 + -161x + 25x2 = 0

Solving
-16 + -161x + 25x2 = 0

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

Divide each side by '25'.
-0.64 + -6.44x + x2 = 0

Move the constant term to the right:

Add '0.64' to each side of the equation.
-0.64 + -6.44x + 0.64 + x2 = 0 + 0.64

Reorder the terms:
-0.64 + 0.64 + -6.44x + x2 = 0 + 0.64

Combine like terms: -0.64 + 0.64 = 0.00
0.00 + -6.44x + x2 = 0 + 0.64
-6.44x + x2 = 0 + 0.64

Combine like terms: 0 + 0.64 = 0.64
-6.44x + x2 = 0.64

The x term is -6.44x.  Take half its coefficient (-3.22).
Square it (10.3684) and add it to both sides.

Add '10.3684' to each side of the equation.
-6.44x + 10.3684 + x2 = 0.64 + 10.3684

Reorder the terms:
10.3684 + -6.44x + x2 = 0.64 + 10.3684

Combine like terms: 0.64 + 10.3684 = 11.0084
10.3684 + -6.44x + x2 = 11.0084

Factor a perfect square on the left side:
(x + -3.22)(x + -3.22) = 11.0084

Calculate the square root of the right side: 3.317890896

Break this problem into two subproblems by setting 
(x + -3.22) equal to 3.317890896 and -3.317890896.


Subproblem 1
x + -3.22 = 3.317890896

Simplifying
x + -3.22 = 3.317890896

Reorder the terms:
-3.22 + x = 3.317890896

Solving
-3.22 + x = 3.317890896

Solving for variable 'x'.

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

Add '3.22' to each side of the equation.
-3.22 + 3.22 + x = 3.317890896 + 3.22

Combine like terms: -3.22 + 3.22 = 0.00
0.00 + x = 3.317890896 + 3.22
x = 3.317890896 + 3.22

Combine like terms: 3.317890896 + 3.22 = 6.537890896
x = 6.537890896

Simplifying
x = 6.537890896


Subproblem 2
x + -3.22 = -3.317890896

Simplifying
x + -3.22 = -3.317890896

Reorder the terms:
-3.22 + x = -3.317890896

Solving
-3.22 + x = -3.317890896

Solving for variable 'x'.

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

Add '3.22' to each side of the equation.
-3.22 + 3.22 + x = -3.317890896 + 3.22

Combine like terms: -3.22 + 3.22 = 0.00
0.00 + x = -3.317890896 + 3.22
x = -3.317890896 + 3.22

Combine like terms: -3.317890896 + 3.22 = -0.097890896
x = -0.097890896

Simplifying
x = -0.097890896


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.537890896, -0.097890896}
Solution
x = {6.537890896, -0.097890896}

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