4x^2-68x+160=0

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Solution for 4x^2-68x+160=0 equation: 


Simplifying
4x2 + -68x + 160 = 0

Reorder the terms:
160 + -68x + 4x2 = 0

Solving
160 + -68x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(40 + -17x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(40 + -17x + x2)' equal to zero and attempt to solve:

Simplifying
40 + -17x + x2 = 0

Solving
40 + -17x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + -17x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + -17x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + -17x + x2 = 0 + -40
-17x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
-17x + x2 = -40

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = -40 + 72.25

Reorder the terms:
72.25 + -17x + x2 = -40 + 72.25

Combine like terms: -40 + 72.25 = 32.25
72.25 + -17x + x2 = 32.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + -8.5) equal to 5.678908346 and -5.678908346.


Subproblem 1
x + -8.5 = 5.678908346

Simplifying
x + -8.5 = 5.678908346

Reorder the terms:
-8.5 + x = 5.678908346

Solving
-8.5 + x = 5.678908346

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = 5.678908346 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 5.678908346 + 8.5
x = 5.678908346 + 8.5

Combine like terms: 5.678908346 + 8.5 = 14.178908346
x = 14.178908346

Simplifying
x = 14.178908346


Subproblem 2
x + -8.5 = -5.678908346

Simplifying
x + -8.5 = -5.678908346

Reorder the terms:
-8.5 + x = -5.678908346

Solving
-8.5 + x = -5.678908346

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = -5.678908346 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -5.678908346 + 8.5
x = -5.678908346 + 8.5

Combine like terms: -5.678908346 + 8.5 = 2.821091654
x = 2.821091654

Simplifying
x = 2.821091654


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.178908346, 2.821091654}
Solution
x = {14.178908346, 2.821091654}

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