64x^2-825x-4786-65x^2=0

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Solution for 64x^2-825x-4786-65x^2=0 equation: 


Simplifying
64x2 + -825x + -4786 + -65x2 = 0

Reorder the terms:
-4786 + -825x + 64x2 + -65x2 = 0

Combine like terms: 64x2 + -65x2 = -1x2
-4786 + -825x + -1x2 = 0

Solving
-4786 + -825x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4786 + 825x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(4786 + 825x + x2)' equal to zero and attempt to solve:

Simplifying
4786 + 825x + x2 = 0

Solving
4786 + 825x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4786' to each side of the equation.
4786 + 825x + -4786 + x2 = 0 + -4786

Reorder the terms:
4786 + -4786 + 825x + x2 = 0 + -4786

Combine like terms: 4786 + -4786 = 0
0 + 825x + x2 = 0 + -4786
825x + x2 = 0 + -4786

Combine like terms: 0 + -4786 = -4786
825x + x2 = -4786

The x term is 825x.  Take half its coefficient (412.5).
Square it (170156.25) and add it to both sides.

Add '170156.25' to each side of the equation.
825x + 170156.25 + x2 = -4786 + 170156.25

Reorder the terms:
170156.25 + 825x + x2 = -4786 + 170156.25

Combine like terms: -4786 + 170156.25 = 165370.25
170156.25 + 825x + x2 = 165370.25

Factor a perfect square on the left side:
(x + 412.5)(x + 412.5) = 165370.25

Calculate the square root of the right side: 406.657411097

Break this problem into two subproblems by setting 
(x + 412.5) equal to 406.657411097 and -406.657411097.


Subproblem 1
x + 412.5 = 406.657411097

Simplifying
x + 412.5 = 406.657411097

Reorder the terms:
412.5 + x = 406.657411097

Solving
412.5 + x = 406.657411097

Solving for variable 'x'.

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

Add '-412.5' to each side of the equation.
412.5 + -412.5 + x = 406.657411097 + -412.5

Combine like terms: 412.5 + -412.5 = 0.0
0.0 + x = 406.657411097 + -412.5
x = 406.657411097 + -412.5

Combine like terms: 406.657411097 + -412.5 = -5.842588903
x = -5.842588903

Simplifying
x = -5.842588903


Subproblem 2
x + 412.5 = -406.657411097

Simplifying
x + 412.5 = -406.657411097

Reorder the terms:
412.5 + x = -406.657411097

Solving
412.5 + x = -406.657411097

Solving for variable 'x'.

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

Add '-412.5' to each side of the equation.
412.5 + -412.5 + x = -406.657411097 + -412.5

Combine like terms: 412.5 + -412.5 = 0.0
0.0 + x = -406.657411097 + -412.5
x = -406.657411097 + -412.5

Combine like terms: -406.657411097 + -412.5 = -819.157411097
x = -819.157411097

Simplifying
x = -819.157411097


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-5.842588903, -819.157411097}
Solution
x = {-5.842588903, -819.157411097}

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