3x^2+200x-10=0

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Solution for 3x^2+200x-10=0 equation: 


Simplifying
3x2 + 200x + -10 = 0

Reorder the terms:
-10 + 200x + 3x2 = 0

Solving
-10 + 200x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-3.333333333 + 66.66666667x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + 66.66666667x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + 66.66666667x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + 66.66666667x + x2 = 0 + 3.333333333
66.66666667x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
66.66666667x + x2 = 3.333333333

The x term is 66.66666667x.  Take half its coefficient (33.33333334).
Square it (1111.111112) and add it to both sides.

Add '1111.111112' to each side of the equation.
66.66666667x + 1111.111112 + x2 = 3.333333333 + 1111.111112

Reorder the terms:
1111.111112 + 66.66666667x + x2 = 3.333333333 + 1111.111112

Combine like terms: 3.333333333 + 1111.111112 = 1114.444445333
1111.111112 + 66.66666667x + x2 = 1114.444445333

Factor a perfect square on the left side:
(x + 33.33333334)(x + 33.33333334) = 1114.444445333

Calculate the square root of the right side: 33.383295903

Break this problem into two subproblems by setting 
(x + 33.33333334) equal to 33.383295903 and -33.383295903.


Subproblem 1
x + 33.33333334 = 33.383295903

Simplifying
x + 33.33333334 = 33.383295903

Reorder the terms:
33.33333334 + x = 33.383295903

Solving
33.33333334 + x = 33.383295903

Solving for variable 'x'.

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

Add '-33.33333334' to each side of the equation.
33.33333334 + -33.33333334 + x = 33.383295903 + -33.33333334

Combine like terms: 33.33333334 + -33.33333334 = 0.00000000
0.00000000 + x = 33.383295903 + -33.33333334
x = 33.383295903 + -33.33333334

Combine like terms: 33.383295903 + -33.33333334 = 0.049962563
x = 0.049962563

Simplifying
x = 0.049962563


Subproblem 2
x + 33.33333334 = -33.383295903

Simplifying
x + 33.33333334 = -33.383295903

Reorder the terms:
33.33333334 + x = -33.383295903

Solving
33.33333334 + x = -33.383295903

Solving for variable 'x'.

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

Add '-33.33333334' to each side of the equation.
33.33333334 + -33.33333334 + x = -33.383295903 + -33.33333334

Combine like terms: 33.33333334 + -33.33333334 = 0.00000000
0.00000000 + x = -33.383295903 + -33.33333334
x = -33.383295903 + -33.33333334

Combine like terms: -33.383295903 + -33.33333334 = -66.716629243
x = -66.716629243

Simplifying
x = -66.716629243


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.049962563, -66.716629243}

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