3x^2+7x-70=0

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Solution for 3x^2+7x-70=0 equation: 


Simplifying
3x2 + 7x + -70 = 0

Reorder the terms:
-70 + 7x + 3x2 = 0

Solving
-70 + 7x + 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 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '23.33333333' to each side of the equation.
-23.33333333 + 2.333333333x + 23.33333333 + x2 = 0 + 23.33333333

Reorder the terms:
-23.33333333 + 23.33333333 + 2.333333333x + x2 = 0 + 23.33333333

Combine like terms: -23.33333333 + 23.33333333 = 0.00000000
0.00000000 + 2.333333333x + x2 = 0 + 23.33333333
2.333333333x + x2 = 0 + 23.33333333

Combine like terms: 0 + 23.33333333 = 23.33333333
2.333333333x + x2 = 23.33333333

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 23.33333333 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 23.33333333 + 1.361111112

Combine like terms: 23.33333333 + 1.361111112 = 24.694444442
1.361111112 + 2.333333333x + x2 = 24.694444442

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 24.694444442

Calculate the square root of the right side: 4.969350505

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 4.969350505 and -4.969350505.


Subproblem 1
x + 1.166666667 = 4.969350505

Simplifying
x + 1.166666667 = 4.969350505

Reorder the terms:
1.166666667 + x = 4.969350505

Solving
1.166666667 + x = 4.969350505

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 4.969350505 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 4.969350505 + -1.166666667
x = 4.969350505 + -1.166666667

Combine like terms: 4.969350505 + -1.166666667 = 3.802683838
x = 3.802683838

Simplifying
x = 3.802683838


Subproblem 2
x + 1.166666667 = -4.969350505

Simplifying
x + 1.166666667 = -4.969350505

Reorder the terms:
1.166666667 + x = -4.969350505

Solving
1.166666667 + x = -4.969350505

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -4.969350505 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -4.969350505 + -1.166666667
x = -4.969350505 + -1.166666667

Combine like terms: -4.969350505 + -1.166666667 = -6.136017172
x = -6.136017172

Simplifying
x = -6.136017172


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.802683838, -6.136017172}

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