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 = 48.33333333
25 + 10x + x2 = 48.33333333

Factor a perfect square on the left side:
(x + 5)(x + 5) = 48.33333333

Calculate the square root of the right side: 6.952217871

Break this problem into two subproblems by setting 
(x + 5) equal to 6.952217871 and -6.952217871.


Subproblem 1
x + 5 = 6.952217871

Simplifying
x + 5 = 6.952217871

Reorder the terms:
5 + x = 6.952217871

Solving
5 + x = 6.952217871

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 = 6.952217871 + -5

Combine like terms: 5 + -5 = 0
0 + x = 6.952217871 + -5
x = 6.952217871 + -5

Combine like terms: 6.952217871 + -5 = 1.952217871
x = 1.952217871

Simplifying
x = 1.952217871


Subproblem 2
x + 5 = -6.952217871

Simplifying
x + 5 = -6.952217871

Reorder the terms:
5 + x = -6.952217871

Solving
5 + x = -6.952217871

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 = -6.952217871 + -5

Combine like terms: 5 + -5 = 0
0 + x = -6.952217871 + -5
x = -6.952217871 + -5

Combine like terms: -6.952217871 + -5 = -11.952217871
x = -11.952217871

Simplifying
x = -11.952217871


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.952217871, -11.952217871}

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