x^2+16x-51=0

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Solution for x^2+16x-51=0 equation: 


Simplifying
x2 + 16x + -51 = 0

Reorder the terms:
-51 + 16x + x2 = 0

Solving
-51 + 16x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + 16x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + 16x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + 16x + x2 = 0 + 51
16x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
16x + x2 = 51

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 = 51 + 64

Reorder the terms:
64 + 16x + x2 = 51 + 64

Combine like terms: 51 + 64 = 115
64 + 16x + x2 = 115

Factor a perfect square on the left side:
(x + 8)(x + 8) = 115

Calculate the square root of the right side: 10.723805295

Break this problem into two subproblems by setting 
(x + 8) equal to 10.723805295 and -10.723805295.


Subproblem 1
x + 8 = 10.723805295

Simplifying
x + 8 = 10.723805295

Reorder the terms:
8 + x = 10.723805295

Solving
8 + x = 10.723805295

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 = 10.723805295 + -8

Combine like terms: 8 + -8 = 0
0 + x = 10.723805295 + -8
x = 10.723805295 + -8

Combine like terms: 10.723805295 + -8 = 2.723805295
x = 2.723805295

Simplifying
x = 2.723805295


Subproblem 2
x + 8 = -10.723805295

Simplifying
x + 8 = -10.723805295

Reorder the terms:
8 + x = -10.723805295

Solving
8 + x = -10.723805295

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 = -10.723805295 + -8

Combine like terms: 8 + -8 = 0
0 + x = -10.723805295 + -8
x = -10.723805295 + -8

Combine like terms: -10.723805295 + -8 = -18.723805295
x = -18.723805295

Simplifying
x = -18.723805295


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.723805295, -18.723805295}

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