x^2+16*x-438.4=0

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Solution for x^2+16*x-438.4=0 equation: 


Simplifying
x2 + 16x + -438.4 = 0

Reorder the terms:
-438.4 + 16x + x2 = 0

Solving
-438.4 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '438.4' to each side of the equation.
-438.4 + 16x + 438.4 + x2 = 0 + 438.4

Reorder the terms:
-438.4 + 438.4 + 16x + x2 = 0 + 438.4

Combine like terms: -438.4 + 438.4 = 0.0
0.0 + 16x + x2 = 0 + 438.4
16x + x2 = 0 + 438.4

Combine like terms: 0 + 438.4 = 438.4
16x + x2 = 438.4

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = 438.4 + 64

Reorder the terms:
64 + 16x + x2 = 438.4 + 64

Combine like terms: 438.4 + 64 = 502.4
64 + 16x + x2 = 502.4

Factor a perfect square on the left side:
(x + 8)(x + 8) = 502.4

Calculate the square root of the right side: 22.414281162

Break this problem into two subproblems by setting 
(x + 8) equal to 22.414281162 and -22.414281162.


Subproblem 1
x + 8 = 22.414281162

Simplifying
x + 8 = 22.414281162

Reorder the terms:
8 + x = 22.414281162

Solving
8 + x = 22.414281162

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 22.414281162 + -8

Combine like terms: 8 + -8 = 0
0 + x = 22.414281162 + -8
x = 22.414281162 + -8

Combine like terms: 22.414281162 + -8 = 14.414281162
x = 14.414281162

Simplifying
x = 14.414281162


Subproblem 2
x + 8 = -22.414281162

Simplifying
x + 8 = -22.414281162

Reorder the terms:
8 + x = -22.414281162

Solving
8 + x = -22.414281162

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -22.414281162 + -8

Combine like terms: 8 + -8 = 0
0 + x = -22.414281162 + -8
x = -22.414281162 + -8

Combine like terms: -22.414281162 + -8 = -30.414281162
x = -30.414281162

Simplifying
x = -30.414281162


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.414281162, -30.414281162}

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