4(x^2-11x-480)=0

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Solution for 4(x^2-11x-480)=0 equation: 


Simplifying
4(x2 + -11x + -480) = 0

Reorder the terms:
4(-480 + -11x + x2) = 0
(-480 * 4 + -11x * 4 + x2 * 4) = 0
(-1920 + -44x + 4x2) = 0

Solving
-1920 + -44x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-480 + -11x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-480 + -11x + x2)' equal to zero and attempt to solve:

Simplifying
-480 + -11x + x2 = 0

Solving
-480 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '480' to each side of the equation.
-480 + -11x + 480 + x2 = 0 + 480

Reorder the terms:
-480 + 480 + -11x + x2 = 0 + 480

Combine like terms: -480 + 480 = 0
0 + -11x + x2 = 0 + 480
-11x + x2 = 0 + 480

Combine like terms: 0 + 480 = 480
-11x + x2 = 480

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = 480 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 480 + 30.25

Combine like terms: 480 + 30.25 = 510.25
30.25 + -11x + x2 = 510.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 510.25

Calculate the square root of the right side: 22.588713996

Break this problem into two subproblems by setting 
(x + -5.5) equal to 22.588713996 and -22.588713996.


Subproblem 1
x + -5.5 = 22.588713996

Simplifying
x + -5.5 = 22.588713996

Reorder the terms:
-5.5 + x = 22.588713996

Solving
-5.5 + x = 22.588713996

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 22.588713996 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 22.588713996 + 5.5
x = 22.588713996 + 5.5

Combine like terms: 22.588713996 + 5.5 = 28.088713996
x = 28.088713996

Simplifying
x = 28.088713996


Subproblem 2
x + -5.5 = -22.588713996

Simplifying
x + -5.5 = -22.588713996

Reorder the terms:
-5.5 + x = -22.588713996

Solving
-5.5 + x = -22.588713996

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -22.588713996 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -22.588713996 + 5.5
x = -22.588713996 + 5.5

Combine like terms: -22.588713996 + 5.5 = -17.088713996
x = -17.088713996

Simplifying
x = -17.088713996


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.088713996, -17.088713996}
Solution
x = {28.088713996, -17.088713996}

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