3x^2+70x-400=0

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Solution for 3x^2+70x-400=0 equation: 


Simplifying
3x2 + 70x + -400 = 0

Reorder the terms:
-400 + 70x + 3x2 = 0

Solving
-400 + 70x + 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'.
-133.3333333 + 23.33333333x + x2 = 0

Move the constant term to the right:

Add '133.3333333' to each side of the equation.
-133.3333333 + 23.33333333x + 133.3333333 + x2 = 0 + 133.3333333

Reorder the terms:
-133.3333333 + 133.3333333 + 23.33333333x + x2 = 0 + 133.3333333

Combine like terms: -133.3333333 + 133.3333333 = 0.0000000
0.0000000 + 23.33333333x + x2 = 0 + 133.3333333
23.33333333x + x2 = 0 + 133.3333333

Combine like terms: 0 + 133.3333333 = 133.3333333
23.33333333x + x2 = 133.3333333

The x term is 23.33333333x.  Take half its coefficient (11.66666667).
Square it (136.1111112) and add it to both sides.

Add '136.1111112' to each side of the equation.
23.33333333x + 136.1111112 + x2 = 133.3333333 + 136.1111112

Reorder the terms:
136.1111112 + 23.33333333x + x2 = 133.3333333 + 136.1111112

Combine like terms: 133.3333333 + 136.1111112 = 269.4444445
136.1111112 + 23.33333333x + x2 = 269.4444445

Factor a perfect square on the left side:
(x + 11.66666667)(x + 11.66666667) = 269.4444445

Calculate the square root of the right side: 16.414763005

Break this problem into two subproblems by setting 
(x + 11.66666667) equal to 16.414763005 and -16.414763005.


Subproblem 1
x + 11.66666667 = 16.414763005

Simplifying
x + 11.66666667 = 16.414763005

Reorder the terms:
11.66666667 + x = 16.414763005

Solving
11.66666667 + x = 16.414763005

Solving for variable 'x'.

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

Add '-11.66666667' to each side of the equation.
11.66666667 + -11.66666667 + x = 16.414763005 + -11.66666667

Combine like terms: 11.66666667 + -11.66666667 = 0.00000000
0.00000000 + x = 16.414763005 + -11.66666667
x = 16.414763005 + -11.66666667

Combine like terms: 16.414763005 + -11.66666667 = 4.748096335
x = 4.748096335

Simplifying
x = 4.748096335


Subproblem 2
x + 11.66666667 = -16.414763005

Simplifying
x + 11.66666667 = -16.414763005

Reorder the terms:
11.66666667 + x = -16.414763005

Solving
11.66666667 + x = -16.414763005

Solving for variable 'x'.

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

Add '-11.66666667' to each side of the equation.
11.66666667 + -11.66666667 + x = -16.414763005 + -11.66666667

Combine like terms: 11.66666667 + -11.66666667 = 0.00000000
0.00000000 + x = -16.414763005 + -11.66666667
x = -16.414763005 + -11.66666667

Combine like terms: -16.414763005 + -11.66666667 = -28.081429675
x = -28.081429675

Simplifying
x = -28.081429675


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.748096335, -28.081429675}

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