2x^2-4x=8x+16

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Solution for 2x^2-4x=8x+16 equation: 


Simplifying
2x2 + -4x = 8x + 16

Reorder the terms:
-4x + 2x2 = 8x + 16

Reorder the terms:
-4x + 2x2 = 16 + 8x

Solving
-4x + 2x2 = 16 + 8x

Solving for variable 'x'.

Reorder the terms:
-16 + -4x + -8x + 2x2 = 16 + 8x + -16 + -8x

Combine like terms: -4x + -8x = -12x
-16 + -12x + 2x2 = 16 + 8x + -16 + -8x

Reorder the terms:
-16 + -12x + 2x2 = 16 + -16 + 8x + -8x

Combine like terms: 16 + -16 = 0
-16 + -12x + 2x2 = 0 + 8x + -8x
-16 + -12x + 2x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-16 + -12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -6x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -6x + x2)' equal to zero and attempt to solve:

Simplifying
-8 + -6x + x2 = 0

Solving
-8 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -6x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -6x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -6x + x2 = 0 + 8
-6x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-6x + x2 = 8

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 8 + 9

Reorder the terms:
9 + -6x + x2 = 8 + 9

Combine like terms: 8 + 9 = 17
9 + -6x + x2 = 17

Factor a perfect square on the left side:
(x + -3)(x + -3) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(x + -3) equal to 4.123105626 and -4.123105626.


Subproblem 1
x + -3 = 4.123105626

Simplifying
x + -3 = 4.123105626

Reorder the terms:
-3 + x = 4.123105626

Solving
-3 + x = 4.123105626

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 4.123105626 + 3

Combine like terms: -3 + 3 = 0
0 + x = 4.123105626 + 3
x = 4.123105626 + 3

Combine like terms: 4.123105626 + 3 = 7.123105626
x = 7.123105626

Simplifying
x = 7.123105626


Subproblem 2
x + -3 = -4.123105626

Simplifying
x + -3 = -4.123105626

Reorder the terms:
-3 + x = -4.123105626

Solving
-3 + x = -4.123105626

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -4.123105626 + 3

Combine like terms: -3 + 3 = 0
0 + x = -4.123105626 + 3
x = -4.123105626 + 3

Combine like terms: -4.123105626 + 3 = -1.123105626
x = -1.123105626

Simplifying
x = -1.123105626


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.123105626, -1.123105626}
Solution
x = {7.123105626, -1.123105626}

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