7x^2-112x+392=0

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Solution for 7x^2-112x+392=0 equation: 


Simplifying
7x2 + -112x + 392 = 0

Reorder the terms:
392 + -112x + 7x2 = 0

Solving
392 + -112x + 7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(56 + -16x + x2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(56 + -16x + x2)' equal to zero and attempt to solve:

Simplifying
56 + -16x + x2 = 0

Solving
56 + -16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-56' to each side of the equation.
56 + -16x + -56 + x2 = 0 + -56

Reorder the terms:
56 + -56 + -16x + x2 = 0 + -56

Combine like terms: 56 + -56 = 0
0 + -16x + x2 = 0 + -56
-16x + x2 = 0 + -56

Combine like terms: 0 + -56 = -56
-16x + x2 = -56

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -56 + 64

Reorder the terms:
64 + -16x + x2 = -56 + 64

Combine like terms: -56 + 64 = 8
64 + -16x + x2 = 8

Factor a perfect square on the left side:
(x + -8)(x + -8) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + -8) equal to 2.828427125 and -2.828427125.


Subproblem 1
x + -8 = 2.828427125

Simplifying
x + -8 = 2.828427125

Reorder the terms:
-8 + x = 2.828427125

Solving
-8 + x = 2.828427125

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 2.828427125 + 8

Combine like terms: -8 + 8 = 0
0 + x = 2.828427125 + 8
x = 2.828427125 + 8

Combine like terms: 2.828427125 + 8 = 10.828427125
x = 10.828427125

Simplifying
x = 10.828427125


Subproblem 2
x + -8 = -2.828427125

Simplifying
x + -8 = -2.828427125

Reorder the terms:
-8 + x = -2.828427125

Solving
-8 + x = -2.828427125

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -2.828427125 + 8

Combine like terms: -8 + 8 = 0
0 + x = -2.828427125 + 8
x = -2.828427125 + 8

Combine like terms: -2.828427125 + 8 = 5.171572875
x = 5.171572875

Simplifying
x = 5.171572875


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.828427125, 5.171572875}
Solution
x = {10.828427125, 5.171572875}

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