4x^2-56x+172=0

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Solution for 4x^2-56x+172=0 equation: 


Simplifying
4x2 + -56x + 172 = 0

Reorder the terms:
172 + -56x + 4x2 = 0

Solving
172 + -56x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(43 + -14x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(43 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
43 + -14x + x2 = 0

Solving
43 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-43' to each side of the equation.
43 + -14x + -43 + x2 = 0 + -43

Reorder the terms:
43 + -43 + -14x + x2 = 0 + -43

Combine like terms: 43 + -43 = 0
0 + -14x + x2 = 0 + -43
-14x + x2 = 0 + -43

Combine like terms: 0 + -43 = -43
-14x + x2 = -43

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 = -43 + 49

Reorder the terms:
49 + -14x + x2 = -43 + 49

Combine like terms: -43 + 49 = 6
49 + -14x + x2 = 6

Factor a perfect square on the left side:
(x + -7)(x + -7) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + -7) equal to 2.449489743 and -2.449489743.


Subproblem 1
x + -7 = 2.449489743

Simplifying
x + -7 = 2.449489743

Reorder the terms:
-7 + x = 2.449489743

Solving
-7 + x = 2.449489743

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 = 2.449489743 + 7

Combine like terms: -7 + 7 = 0
0 + x = 2.449489743 + 7
x = 2.449489743 + 7

Combine like terms: 2.449489743 + 7 = 9.449489743
x = 9.449489743

Simplifying
x = 9.449489743


Subproblem 2
x + -7 = -2.449489743

Simplifying
x + -7 = -2.449489743

Reorder the terms:
-7 + x = -2.449489743

Solving
-7 + x = -2.449489743

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 = -2.449489743 + 7

Combine like terms: -7 + 7 = 0
0 + x = -2.449489743 + 7
x = -2.449489743 + 7

Combine like terms: -2.449489743 + 7 = 4.550510257
x = 4.550510257

Simplifying
x = 4.550510257


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.449489743, 4.550510257}
Solution
x = {9.449489743, 4.550510257}

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