3x^2+30x-152=0

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Solution for 3x^2+30x-152=0 equation: 


Simplifying
3x2 + 30x + -152 = 0

Reorder the terms:
-152 + 30x + 3x2 = 0

Solving
-152 + 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'.
-50.66666667 + 10x + x2 = 0

Move the constant term to the right:

Add '50.66666667' to each side of the equation.
-50.66666667 + 10x + 50.66666667 + x2 = 0 + 50.66666667

Reorder the terms:
-50.66666667 + 50.66666667 + 10x + x2 = 0 + 50.66666667

Combine like terms: -50.66666667 + 50.66666667 = 0.00000000
0.00000000 + 10x + x2 = 0 + 50.66666667
10x + x2 = 0 + 50.66666667

Combine like terms: 0 + 50.66666667 = 50.66666667
10x + x2 = 50.66666667

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 = 50.66666667 + 25

Reorder the terms:
25 + 10x + x2 = 50.66666667 + 25

Combine like terms: 50.66666667 + 25 = 75.66666667
25 + 10x + x2 = 75.66666667

Factor a perfect square on the left side:
(x + 5)(x + 5) = 75.66666667

Calculate the square root of the right side: 8.698658901

Break this problem into two subproblems by setting 
(x + 5) equal to 8.698658901 and -8.698658901.


Subproblem 1
x + 5 = 8.698658901

Simplifying
x + 5 = 8.698658901

Reorder the terms:
5 + x = 8.698658901

Solving
5 + x = 8.698658901

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 = 8.698658901 + -5

Combine like terms: 5 + -5 = 0
0 + x = 8.698658901 + -5
x = 8.698658901 + -5

Combine like terms: 8.698658901 + -5 = 3.698658901
x = 3.698658901

Simplifying
x = 3.698658901


Subproblem 2
x + 5 = -8.698658901

Simplifying
x + 5 = -8.698658901

Reorder the terms:
5 + x = -8.698658901

Solving
5 + x = -8.698658901

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 = -8.698658901 + -5

Combine like terms: 5 + -5 = 0
0 + x = -8.698658901 + -5
x = -8.698658901 + -5

Combine like terms: -8.698658901 + -5 = -13.698658901
x = -13.698658901

Simplifying
x = -13.698658901


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.698658901, -13.698658901}

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