4x^2-56x+112=0

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Solution for 4x^2-56x+112=0 equation: 


Simplifying
4x2 + -56x + 112 = 0

Reorder the terms:
112 + -56x + 4x2 = 0

Solving
112 + -56x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(28 + -14x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(28 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
28 + -14x + x2 = 0

Solving
28 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + -14x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + -14x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + -14x + x2 = 0 + -28
-14x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
-14x + x2 = -28

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -28 + 49

Reorder the terms:
49 + -14x + x2 = -28 + 49

Combine like terms: -28 + 49 = 21
49 + -14x + x2 = 21

Factor a perfect square on the left side:
(x + -7)(x + -7) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + -7) equal to 4.582575695 and -4.582575695.


Subproblem 1
x + -7 = 4.582575695

Simplifying
x + -7 = 4.582575695

Reorder the terms:
-7 + x = 4.582575695

Solving
-7 + x = 4.582575695

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 4.582575695 + 7

Combine like terms: -7 + 7 = 0
0 + x = 4.582575695 + 7
x = 4.582575695 + 7

Combine like terms: 4.582575695 + 7 = 11.582575695
x = 11.582575695

Simplifying
x = 11.582575695


Subproblem 2
x + -7 = -4.582575695

Simplifying
x + -7 = -4.582575695

Reorder the terms:
-7 + x = -4.582575695

Solving
-7 + x = -4.582575695

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -4.582575695 + 7

Combine like terms: -7 + 7 = 0
0 + x = -4.582575695 + 7
x = -4.582575695 + 7

Combine like terms: -4.582575695 + 7 = 2.417424305
x = 2.417424305

Simplifying
x = 2.417424305


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.582575695, 2.417424305}
Solution
x = {11.582575695, 2.417424305}

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