4x^2-44x+112=1200

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Solution for 4x^2-44x+112=1200 equation: 


Simplifying
4x2 + -44x + 112 = 1200

Reorder the terms:
112 + -44x + 4x2 = 1200

Solving
112 + -44x + 4x2 = 1200

Solving for variable 'x'.

Reorder the terms:
112 + -1200 + -44x + 4x2 = 1200 + -1200

Combine like terms: 112 + -1200 = -1088
-1088 + -44x + 4x2 = 1200 + -1200

Combine like terms: 1200 + -1200 = 0
-1088 + -44x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-272 + -11x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-272 + -11x + x2)' equal to zero and attempt to solve:

Simplifying
-272 + -11x + x2 = 0

Solving
-272 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '272' to each side of the equation.
-272 + -11x + 272 + x2 = 0 + 272

Reorder the terms:
-272 + 272 + -11x + x2 = 0 + 272

Combine like terms: -272 + 272 = 0
0 + -11x + x2 = 0 + 272
-11x + x2 = 0 + 272

Combine like terms: 0 + 272 = 272
-11x + x2 = 272

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 = 272 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 272 + 30.25

Combine like terms: 272 + 30.25 = 302.25
30.25 + -11x + x2 = 302.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 302.25

Calculate the square root of the right side: 17.385338651

Break this problem into two subproblems by setting 
(x + -5.5) equal to 17.385338651 and -17.385338651.


Subproblem 1
x + -5.5 = 17.385338651

Simplifying
x + -5.5 = 17.385338651

Reorder the terms:
-5.5 + x = 17.385338651

Solving
-5.5 + x = 17.385338651

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 = 17.385338651 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 17.385338651 + 5.5
x = 17.385338651 + 5.5

Combine like terms: 17.385338651 + 5.5 = 22.885338651
x = 22.885338651

Simplifying
x = 22.885338651


Subproblem 2
x + -5.5 = -17.385338651

Simplifying
x + -5.5 = -17.385338651

Reorder the terms:
-5.5 + x = -17.385338651

Solving
-5.5 + x = -17.385338651

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 = -17.385338651 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -17.385338651 + 5.5
x = -17.385338651 + 5.5

Combine like terms: -17.385338651 + 5.5 = -11.885338651
x = -11.885338651

Simplifying
x = -11.885338651


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.885338651, -11.885338651}
Solution
x = {22.885338651, -11.885338651}

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