3x^2+70x-552=0

Solution for 3x^2+70x-552=0 equation:

Simplifying
3x2 + 70x + -552 = 0

Reorder the terms:
-552 + 70x + 3x2 = 0

Solving
-552 + 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'.
-184 + 23.33333333x + x2 = 0

Move the constant term to the right:

Add '184' to each side of the equation.
-184 + 23.33333333x + 184 + x2 = 0 + 184

Reorder the terms:
-184 + 184 + 23.33333333x + x2 = 0 + 184

Combine like terms: -184 + 184 = 0
0 + 23.33333333x + x2 = 0 + 184
23.33333333x + x2 = 0 + 184

Combine like terms: 0 + 184 = 184
23.33333333x + x2 = 184

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 = 184 + 136.1111112

Reorder the terms:
136.1111112 + 23.33333333x + x2 = 184 + 136.1111112

Combine like terms: 184 + 136.1111112 = 320.1111112
136.1111112 + 23.33333333x + x2 = 320.1111112

Factor a perfect square on the left side:
(x + 11.66666667)(x + 11.66666667) = 320.1111112

Calculate the square root of the right side: 17.891649203

Break this problem into two subproblems by setting 
(x + 11.66666667) equal to 17.891649203 and -17.891649203.

Subproblem 1
x + 11.66666667 = 17.891649203

Simplifying
x + 11.66666667 = 17.891649203

Reorder the terms:
11.66666667 + x = 17.891649203

Solving
11.66666667 + x = 17.891649203

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 = 17.891649203 + -11.66666667

Combine like terms: 11.66666667 + -11.66666667 = 0.00000000
0.00000000 + x = 17.891649203 + -11.66666667
x = 17.891649203 + -11.66666667

Combine like terms: 17.891649203 + -11.66666667 = 6.224982533
x = 6.224982533

Simplifying
x = 6.224982533

Subproblem 2
x + 11.66666667 = -17.891649203

Simplifying
x + 11.66666667 = -17.891649203

Reorder the terms:
11.66666667 + x = -17.891649203

Solving
11.66666667 + x = -17.891649203

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 = -17.891649203 + -11.66666667

Combine like terms: 11.66666667 + -11.66666667 = 0.00000000
0.00000000 + x = -17.891649203 + -11.66666667
x = -17.891649203 + -11.66666667

Combine like terms: -17.891649203 + -11.66666667 = -29.558315873
x = -29.558315873

Simplifying
x = -29.558315873

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.224982533, -29.558315873}