9.8x^2+6x-100=0

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Solution for 9.8x^2+6x-100=0 equation: 


Simplifying
9.8x2 + 6x + -100 = 0

Reorder the terms:
-100 + 6x + 9.8x2 = 0

Solving
-100 + 6x + 9.8x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
9.8 the coefficient of the squared term: 

Divide each side by '9.8'.
-10.20408163 + 0.612244898x + x2 = 0

Move the constant term to the right:

Add '10.20408163' to each side of the equation.
-10.20408163 + 0.612244898x + 10.20408163 + x2 = 0 + 10.20408163

Reorder the terms:
-10.20408163 + 10.20408163 + 0.612244898x + x2 = 0 + 10.20408163

Combine like terms: -10.20408163 + 10.20408163 = 0.00000000
0.00000000 + 0.612244898x + x2 = 0 + 10.20408163
0.612244898x + x2 = 0 + 10.20408163

Combine like terms: 0 + 10.20408163 = 10.20408163
0.612244898x + x2 = 10.20408163

The x term is 0.612244898x.  Take half its coefficient (0.306122449).
Square it (0.09371095378) and add it to both sides.

Add '0.09371095378' to each side of the equation.
0.612244898x + 0.09371095378 + x2 = 10.20408163 + 0.09371095378

Reorder the terms:
0.09371095378 + 0.612244898x + x2 = 10.20408163 + 0.09371095378

Combine like terms: 10.20408163 + 0.09371095378 = 10.29779258378
0.09371095378 + 0.612244898x + x2 = 10.29779258378

Factor a perfect square on the left side:
(x + 0.306122449)(x + 0.306122449) = 10.29779258378

Calculate the square root of the right side: 3.209017386

Break this problem into two subproblems by setting 
(x + 0.306122449) equal to 3.209017386 and -3.209017386.


Subproblem 1
x + 0.306122449 = 3.209017386

Simplifying
x + 0.306122449 = 3.209017386

Reorder the terms:
0.306122449 + x = 3.209017386

Solving
0.306122449 + x = 3.209017386

Solving for variable 'x'.

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

Add '-0.306122449' to each side of the equation.
0.306122449 + -0.306122449 + x = 3.209017386 + -0.306122449

Combine like terms: 0.306122449 + -0.306122449 = 0.000000000
0.000000000 + x = 3.209017386 + -0.306122449
x = 3.209017386 + -0.306122449

Combine like terms: 3.209017386 + -0.306122449 = 2.902894937
x = 2.902894937

Simplifying
x = 2.902894937


Subproblem 2
x + 0.306122449 = -3.209017386

Simplifying
x + 0.306122449 = -3.209017386

Reorder the terms:
0.306122449 + x = -3.209017386

Solving
0.306122449 + x = -3.209017386

Solving for variable 'x'.

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

Add '-0.306122449' to each side of the equation.
0.306122449 + -0.306122449 + x = -3.209017386 + -0.306122449

Combine like terms: 0.306122449 + -0.306122449 = 0.000000000
0.000000000 + x = -3.209017386 + -0.306122449
x = -3.209017386 + -0.306122449

Combine like terms: -3.209017386 + -0.306122449 = -3.515139835
x = -3.515139835

Simplifying
x = -3.515139835


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.902894937, -3.515139835}

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