x^2+7x-16800=0

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Solution for x^2+7x-16800=0 equation: 


Simplifying
x2 + 7x + -16800 = 0

Reorder the terms:
-16800 + 7x + x2 = 0

Solving
-16800 + 7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '16800' to each side of the equation.
-16800 + 7x + 16800 + x2 = 0 + 16800

Reorder the terms:
-16800 + 16800 + 7x + x2 = 0 + 16800

Combine like terms: -16800 + 16800 = 0
0 + 7x + x2 = 0 + 16800
7x + x2 = 0 + 16800

Combine like terms: 0 + 16800 = 16800
7x + x2 = 16800

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 16800 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 16800 + 12.25

Combine like terms: 16800 + 12.25 = 16812.25
12.25 + 7x + x2 = 16812.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 16812.25

Calculate the square root of the right side: 129.662060758

Break this problem into two subproblems by setting 
(x + 3.5) equal to 129.662060758 and -129.662060758.


Subproblem 1
x + 3.5 = 129.662060758

Simplifying
x + 3.5 = 129.662060758

Reorder the terms:
3.5 + x = 129.662060758

Solving
3.5 + x = 129.662060758

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 129.662060758 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 129.662060758 + -3.5
x = 129.662060758 + -3.5

Combine like terms: 129.662060758 + -3.5 = 126.162060758
x = 126.162060758

Simplifying
x = 126.162060758


Subproblem 2
x + 3.5 = -129.662060758

Simplifying
x + 3.5 = -129.662060758

Reorder the terms:
3.5 + x = -129.662060758

Solving
3.5 + x = -129.662060758

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -129.662060758 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -129.662060758 + -3.5
x = -129.662060758 + -3.5

Combine like terms: -129.662060758 + -3.5 = -133.162060758
x = -133.162060758

Simplifying
x = -133.162060758


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {126.162060758, -133.162060758}

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