170=x*(2x-4)

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Solution for 170=x*(2x-4) equation: 


Simplifying
170 = x(2x + -4)

Reorder the terms:
170 = x(-4 + 2x)
170 = (-4 * x + 2x * x)
170 = (-4x + 2x2)

Solving
170 = -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
170 + 4x + -2x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
170 + 4x + -2x2 = 0 + 2x2 + -2x2
170 + 4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
170 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(85 + 2x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(85 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
85 + 2x + -1x2 = 0

Solving
85 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-85 + -2x + x2 = 0

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + -2x + 85 + x2 = 0 + 85

Reorder the terms:
-85 + 85 + -2x + x2 = 0 + 85

Combine like terms: -85 + 85 = 0
0 + -2x + x2 = 0 + 85
-2x + x2 = 0 + 85

Combine like terms: 0 + 85 = 85
-2x + x2 = 85

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 85 + 1

Reorder the terms:
1 + -2x + x2 = 85 + 1

Combine like terms: 85 + 1 = 86
1 + -2x + x2 = 86

Factor a perfect square on the left side:
(x + -1)(x + -1) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(x + -1) equal to 9.273618495 and -9.273618495.


Subproblem 1
x + -1 = 9.273618495

Simplifying
x + -1 = 9.273618495

Reorder the terms:
-1 + x = 9.273618495

Solving
-1 + x = 9.273618495

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 9.273618495 + 1

Combine like terms: -1 + 1 = 0
0 + x = 9.273618495 + 1
x = 9.273618495 + 1

Combine like terms: 9.273618495 + 1 = 10.273618495
x = 10.273618495

Simplifying
x = 10.273618495


Subproblem 2
x + -1 = -9.273618495

Simplifying
x + -1 = -9.273618495

Reorder the terms:
-1 + x = -9.273618495

Solving
-1 + x = -9.273618495

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -9.273618495 + 1

Combine like terms: -1 + 1 = 0
0 + x = -9.273618495 + 1
x = -9.273618495 + 1

Combine like terms: -9.273618495 + 1 = -8.273618495
x = -8.273618495

Simplifying
x = -8.273618495


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.273618495, -8.273618495}
Solution
x = {10.273618495, -8.273618495}

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