x^2-(-16x)+40=0

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Solution for x^2-(-16x)+40=0 equation: 


Simplifying
x2 + -1(-16x) + 40 = 0

Remove parenthesis around (-16x)
x2 + -1 * -16x + 40 = 0

Multiply -1 * -16
x2 + 16x + 40 = 0

Reorder the terms:
40 + 16x + x2 = 0

Solving
40 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + 16x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + 16x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + 16x + x2 = 0 + -40
16x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
16x + x2 = -40

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 = -40 + 64

Reorder the terms:
64 + 16x + x2 = -40 + 64

Combine like terms: -40 + 64 = 24
64 + 16x + x2 = 24

Factor a perfect square on the left side:
(x + 8)(x + 8) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + 8) equal to 4.898979486 and -4.898979486.


Subproblem 1
x + 8 = 4.898979486

Simplifying
x + 8 = 4.898979486

Reorder the terms:
8 + x = 4.898979486

Solving
8 + x = 4.898979486

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 = 4.898979486 + -8

Combine like terms: 8 + -8 = 0
0 + x = 4.898979486 + -8
x = 4.898979486 + -8

Combine like terms: 4.898979486 + -8 = -3.101020514
x = -3.101020514

Simplifying
x = -3.101020514


Subproblem 2
x + 8 = -4.898979486

Simplifying
x + 8 = -4.898979486

Reorder the terms:
8 + x = -4.898979486

Solving
8 + x = -4.898979486

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 = -4.898979486 + -8

Combine like terms: 8 + -8 = 0
0 + x = -4.898979486 + -8
x = -4.898979486 + -8

Combine like terms: -4.898979486 + -8 = -12.898979486
x = -12.898979486

Simplifying
x = -12.898979486


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.101020514, -12.898979486}

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