4x^2-52x-480=0

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Solution for 4x^2-52x-480=0 equation: 


Simplifying
4x2 + -52x + -480 = 0

Reorder the terms:
-480 + -52x + 4x2 = 0

Solving
-480 + -52x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-120 + -13x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-120 + -13x + x2)' equal to zero and attempt to solve:

Simplifying
-120 + -13x + x2 = 0

Solving
-120 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + -13x + 120 + x2 = 0 + 120

Reorder the terms:
-120 + 120 + -13x + x2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + -13x + x2 = 0 + 120
-13x + x2 = 0 + 120

Combine like terms: 0 + 120 = 120
-13x + x2 = 120

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 120 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 120 + 42.25

Combine like terms: 120 + 42.25 = 162.25
42.25 + -13x + x2 = 162.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 162.25

Calculate the square root of the right side: 12.737739203

Break this problem into two subproblems by setting 
(x + -6.5) equal to 12.737739203 and -12.737739203.


Subproblem 1
x + -6.5 = 12.737739203

Simplifying
x + -6.5 = 12.737739203

Reorder the terms:
-6.5 + x = 12.737739203

Solving
-6.5 + x = 12.737739203

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 12.737739203 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 12.737739203 + 6.5
x = 12.737739203 + 6.5

Combine like terms: 12.737739203 + 6.5 = 19.237739203
x = 19.237739203

Simplifying
x = 19.237739203


Subproblem 2
x + -6.5 = -12.737739203

Simplifying
x + -6.5 = -12.737739203

Reorder the terms:
-6.5 + x = -12.737739203

Solving
-6.5 + x = -12.737739203

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -12.737739203 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -12.737739203 + 6.5
x = -12.737739203 + 6.5

Combine like terms: -12.737739203 + 6.5 = -6.237739203
x = -6.237739203

Simplifying
x = -6.237739203


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.237739203, -6.237739203}
Solution
x = {19.237739203, -6.237739203}

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