3x^2+30x-48=0

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Solution for 3x^2+30x-48=0 equation: 


Simplifying
3x2 + 30x + -48 = 0

Reorder the terms:
-48 + 30x + 3x2 = 0

Solving
-48 + 30x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-16 + 10x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-16 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + 10x + x2 = 0

Solving
-16 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 10x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 10x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 10x + x2 = 0 + 16
10x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
10x + x2 = 16

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 = 16 + 25

Reorder the terms:
25 + 10x + x2 = 16 + 25

Combine like terms: 16 + 25 = 41
25 + 10x + x2 = 41

Factor a perfect square on the left side:
(x + 5)(x + 5) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + 5) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + 5 = 6.403124237

Simplifying
x + 5 = 6.403124237

Reorder the terms:
5 + x = 6.403124237

Solving
5 + x = 6.403124237

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 = 6.403124237 + -5

Combine like terms: 5 + -5 = 0
0 + x = 6.403124237 + -5
x = 6.403124237 + -5

Combine like terms: 6.403124237 + -5 = 1.403124237
x = 1.403124237

Simplifying
x = 1.403124237


Subproblem 2
x + 5 = -6.403124237

Simplifying
x + 5 = -6.403124237

Reorder the terms:
5 + x = -6.403124237

Solving
5 + x = -6.403124237

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 = -6.403124237 + -5

Combine like terms: 5 + -5 = 0
0 + x = -6.403124237 + -5
x = -6.403124237 + -5

Combine like terms: -6.403124237 + -5 = -11.403124237
x = -11.403124237

Simplifying
x = -11.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.403124237, -11.403124237}
Solution
x = {1.403124237, -11.403124237}

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