3x^2+30x+70=0

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Solution for 3x^2+30x+70=0 equation: 


Simplifying
3x2 + 30x + 70 = 0

Reorder the terms:
70 + 30x + 3x2 = 0

Solving
70 + 30x + 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'.
23.33333333 + 10x + x2 = 0

Move the constant term to the right:

Add '-23.33333333' to each side of the equation.
23.33333333 + 10x + -23.33333333 + x2 = 0 + -23.33333333

Reorder the terms:
23.33333333 + -23.33333333 + 10x + x2 = 0 + -23.33333333

Combine like terms: 23.33333333 + -23.33333333 = 0.00000000
0.00000000 + 10x + x2 = 0 + -23.33333333
10x + x2 = 0 + -23.33333333

Combine like terms: 0 + -23.33333333 = -23.33333333
10x + x2 = -23.33333333

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -23.33333333 + 25

Reorder the terms:
25 + 10x + x2 = -23.33333333 + 25

Combine like terms: -23.33333333 + 25 = 1.66666667
25 + 10x + x2 = 1.66666667

Factor a perfect square on the left side:
(x + 5)(x + 5) = 1.66666667

Calculate the square root of the right side: 1.29099445

Break this problem into two subproblems by setting 
(x + 5) equal to 1.29099445 and -1.29099445.


Subproblem 1
x + 5 = 1.29099445

Simplifying
x + 5 = 1.29099445

Reorder the terms:
5 + x = 1.29099445

Solving
5 + x = 1.29099445

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 1.29099445 + -5

Combine like terms: 5 + -5 = 0
0 + x = 1.29099445 + -5
x = 1.29099445 + -5

Combine like terms: 1.29099445 + -5 = -3.70900555
x = -3.70900555

Simplifying
x = -3.70900555


Subproblem 2
x + 5 = -1.29099445

Simplifying
x + 5 = -1.29099445

Reorder the terms:
5 + x = -1.29099445

Solving
5 + x = -1.29099445

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -1.29099445 + -5

Combine like terms: 5 + -5 = 0
0 + x = -1.29099445 + -5
x = -1.29099445 + -5

Combine like terms: -1.29099445 + -5 = -6.29099445
x = -6.29099445

Simplifying
x = -6.29099445


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.70900555, -6.29099445}

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