4(4x)+2(x^2)=336

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Solution for 4(4x)+2(x^2)=336 equation: 


Simplifying
4(4x) + 2(x2) = 336

Remove parenthesis around (4x)
4 * 4x + 2(x2) = 336

Multiply 4 * 4
16x + 2(x2) = 336

Solving
16x + 2x2 = 336

Solving for variable 'x'.

Reorder the terms:
-336 + 16x + 2x2 = 336 + -336

Combine like terms: 336 + -336 = 0
-336 + 16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-168 + 8x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-168 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
-168 + 8x + x2 = 0

Solving
-168 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '168' to each side of the equation.
-168 + 8x + 168 + x2 = 0 + 168

Reorder the terms:
-168 + 168 + 8x + x2 = 0 + 168

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

Combine like terms: 0 + 168 = 168
8x + x2 = 168

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 168 + 16

Reorder the terms:
16 + 8x + x2 = 168 + 16

Combine like terms: 168 + 16 = 184
16 + 8x + x2 = 184

Factor a perfect square on the left side:
(x + 4)(x + 4) = 184

Calculate the square root of the right side: 13.564659966

Break this problem into two subproblems by setting 
(x + 4) equal to 13.564659966 and -13.564659966.


Subproblem 1
x + 4 = 13.564659966

Simplifying
x + 4 = 13.564659966

Reorder the terms:
4 + x = 13.564659966

Solving
4 + x = 13.564659966

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 13.564659966 + -4

Combine like terms: 4 + -4 = 0
0 + x = 13.564659966 + -4
x = 13.564659966 + -4

Combine like terms: 13.564659966 + -4 = 9.564659966
x = 9.564659966

Simplifying
x = 9.564659966


Subproblem 2
x + 4 = -13.564659966

Simplifying
x + 4 = -13.564659966

Reorder the terms:
4 + x = -13.564659966

Solving
4 + x = -13.564659966

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -13.564659966 + -4

Combine like terms: 4 + -4 = 0
0 + x = -13.564659966 + -4
x = -13.564659966 + -4

Combine like terms: -13.564659966 + -4 = -17.564659966
x = -17.564659966

Simplifying
x = -17.564659966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.564659966, -17.564659966}
Solution
x = {9.564659966, -17.564659966}

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