x^2+16x-840=0

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Solution for x^2+16x-840=0 equation: 


Simplifying
x2 + 16x + -840 = 0

Reorder the terms:
-840 + 16x + x2 = 0

Solving
-840 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '840' to each side of the equation.
-840 + 16x + 840 + x2 = 0 + 840

Reorder the terms:
-840 + 840 + 16x + x2 = 0 + 840

Combine like terms: -840 + 840 = 0
0 + 16x + x2 = 0 + 840
16x + x2 = 0 + 840

Combine like terms: 0 + 840 = 840
16x + x2 = 840

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 = 840 + 64

Reorder the terms:
64 + 16x + x2 = 840 + 64

Combine like terms: 840 + 64 = 904
64 + 16x + x2 = 904

Factor a perfect square on the left side:
(x + 8)(x + 8) = 904

Calculate the square root of the right side: 30.066592757

Break this problem into two subproblems by setting 
(x + 8) equal to 30.066592757 and -30.066592757.


Subproblem 1
x + 8 = 30.066592757

Simplifying
x + 8 = 30.066592757

Reorder the terms:
8 + x = 30.066592757

Solving
8 + x = 30.066592757

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 = 30.066592757 + -8

Combine like terms: 8 + -8 = 0
0 + x = 30.066592757 + -8
x = 30.066592757 + -8

Combine like terms: 30.066592757 + -8 = 22.066592757
x = 22.066592757

Simplifying
x = 22.066592757


Subproblem 2
x + 8 = -30.066592757

Simplifying
x + 8 = -30.066592757

Reorder the terms:
8 + x = -30.066592757

Solving
8 + x = -30.066592757

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 = -30.066592757 + -8

Combine like terms: 8 + -8 = 0
0 + x = -30.066592757 + -8
x = -30.066592757 + -8

Combine like terms: -30.066592757 + -8 = -38.066592757
x = -38.066592757

Simplifying
x = -38.066592757


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.066592757, -38.066592757}

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