18+2x(x-4)=168

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Solution for 18+2x(x-4)=168 equation: 


Simplifying
18 + 2x(x + -4) = 168

Reorder the terms:
18 + 2x(-4 + x) = 168
18 + (-4 * 2x + x * 2x) = 168
18 + (-8x + 2x2) = 168

Solving
18 + -8x + 2x2 = 168

Solving for variable 'x'.

Reorder the terms:
18 + -168 + -8x + 2x2 = 168 + -168

Combine like terms: 18 + -168 = -150
-150 + -8x + 2x2 = 168 + -168

Combine like terms: 168 + -168 = 0
-150 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-75 + -4x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-75 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-75 + -4x + x2 = 0

Solving
-75 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + -4x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + -4x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + -4x + x2 = 0 + 75
-4x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
-4x + x2 = 75

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 75 + 4

Reorder the terms:
4 + -4x + x2 = 75 + 4

Combine like terms: 75 + 4 = 79
4 + -4x + x2 = 79

Factor a perfect square on the left side:
(x + -2)(x + -2) = 79

Calculate the square root of the right side: 8.888194417

Break this problem into two subproblems by setting 
(x + -2) equal to 8.888194417 and -8.888194417.


Subproblem 1
x + -2 = 8.888194417

Simplifying
x + -2 = 8.888194417

Reorder the terms:
-2 + x = 8.888194417

Solving
-2 + x = 8.888194417

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 8.888194417 + 2

Combine like terms: -2 + 2 = 0
0 + x = 8.888194417 + 2
x = 8.888194417 + 2

Combine like terms: 8.888194417 + 2 = 10.888194417
x = 10.888194417

Simplifying
x = 10.888194417


Subproblem 2
x + -2 = -8.888194417

Simplifying
x + -2 = -8.888194417

Reorder the terms:
-2 + x = -8.888194417

Solving
-2 + x = -8.888194417

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -8.888194417 + 2

Combine like terms: -2 + 2 = 0
0 + x = -8.888194417 + 2
x = -8.888194417 + 2

Combine like terms: -8.888194417 + 2 = -6.888194417
x = -6.888194417

Simplifying
x = -6.888194417


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.888194417, -6.888194417}
Solution
x = {10.888194417, -6.888194417}

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