3x^2+100x-700=0

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Solution for 3x^2+100x-700=0 equation: 


Simplifying
3x2 + 100x + -700 = 0

Reorder the terms:
-700 + 100x + 3x2 = 0

Solving
-700 + 100x + 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'.
-233.3333333 + 33.33333333x + x2 = 0

Move the constant term to the right:

Add '233.3333333' to each side of the equation.
-233.3333333 + 33.33333333x + 233.3333333 + x2 = 0 + 233.3333333

Reorder the terms:
-233.3333333 + 233.3333333 + 33.33333333x + x2 = 0 + 233.3333333

Combine like terms: -233.3333333 + 233.3333333 = 0.0000000
0.0000000 + 33.33333333x + x2 = 0 + 233.3333333
33.33333333x + x2 = 0 + 233.3333333

Combine like terms: 0 + 233.3333333 = 233.3333333
33.33333333x + x2 = 233.3333333

The x term is 33.33333333x.  Take half its coefficient (16.66666667).
Square it (277.7777779) and add it to both sides.

Add '277.7777779' to each side of the equation.
33.33333333x + 277.7777779 + x2 = 233.3333333 + 277.7777779

Reorder the terms:
277.7777779 + 33.33333333x + x2 = 233.3333333 + 277.7777779

Combine like terms: 233.3333333 + 277.7777779 = 511.1111112
277.7777779 + 33.33333333x + x2 = 511.1111112

Factor a perfect square on the left side:
(x + 16.66666667)(x + 16.66666667) = 511.1111112

Calculate the square root of the right side: 22.607766612

Break this problem into two subproblems by setting 
(x + 16.66666667) equal to 22.607766612 and -22.607766612.


Subproblem 1
x + 16.66666667 = 22.607766612

Simplifying
x + 16.66666667 = 22.607766612

Reorder the terms:
16.66666667 + x = 22.607766612

Solving
16.66666667 + x = 22.607766612

Solving for variable 'x'.

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

Add '-16.66666667' to each side of the equation.
16.66666667 + -16.66666667 + x = 22.607766612 + -16.66666667

Combine like terms: 16.66666667 + -16.66666667 = 0.00000000
0.00000000 + x = 22.607766612 + -16.66666667
x = 22.607766612 + -16.66666667

Combine like terms: 22.607766612 + -16.66666667 = 5.941099942
x = 5.941099942

Simplifying
x = 5.941099942


Subproblem 2
x + 16.66666667 = -22.607766612

Simplifying
x + 16.66666667 = -22.607766612

Reorder the terms:
16.66666667 + x = -22.607766612

Solving
16.66666667 + x = -22.607766612

Solving for variable 'x'.

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

Add '-16.66666667' to each side of the equation.
16.66666667 + -16.66666667 + x = -22.607766612 + -16.66666667

Combine like terms: 16.66666667 + -16.66666667 = 0.00000000
0.00000000 + x = -22.607766612 + -16.66666667
x = -22.607766612 + -16.66666667

Combine like terms: -22.607766612 + -16.66666667 = -39.274433282
x = -39.274433282

Simplifying
x = -39.274433282


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.941099942, -39.274433282}

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