-3x^2-24x-46=0

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Solution for -3x^2-24x-46=0 equation: 


Simplifying
-3x2 + -24x + -46 = 0

Reorder the terms:
-46 + -24x + -3x2 = 0

Solving
-46 + -24x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(46 + 24x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(46 + 24x + 3x2)' equal to zero and attempt to solve:

Simplifying
46 + 24x + 3x2 = 0

Solving
46 + 24x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
15.33333333 + 8x + x2 = 0

Move the constant term to the right:

Add '-15.33333333' to each side of the equation.
15.33333333 + 8x + -15.33333333 + x2 = 0 + -15.33333333

Reorder the terms:
15.33333333 + -15.33333333 + 8x + x2 = 0 + -15.33333333

Combine like terms: 15.33333333 + -15.33333333 = 0.00000000
0.00000000 + 8x + x2 = 0 + -15.33333333
8x + x2 = 0 + -15.33333333

Combine like terms: 0 + -15.33333333 = -15.33333333
8x + x2 = -15.33333333

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -15.33333333 + 16

Reorder the terms:
16 + 8x + x2 = -15.33333333 + 16

Combine like terms: -15.33333333 + 16 = 0.66666667
16 + 8x + x2 = 0.66666667

Factor a perfect square on the left side:
(x + 4)(x + 4) = 0.66666667

Calculate the square root of the right side: 0.816496583

Break this problem into two subproblems by setting 
(x + 4) equal to 0.816496583 and -0.816496583.


Subproblem 1
x + 4 = 0.816496583

Simplifying
x + 4 = 0.816496583

Reorder the terms:
4 + x = 0.816496583

Solving
4 + x = 0.816496583

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 0.816496583 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0.816496583 + -4
x = 0.816496583 + -4

Combine like terms: 0.816496583 + -4 = -3.183503417
x = -3.183503417

Simplifying
x = -3.183503417


Subproblem 2
x + 4 = -0.816496583

Simplifying
x + 4 = -0.816496583

Reorder the terms:
4 + x = -0.816496583

Solving
4 + x = -0.816496583

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -0.816496583 + -4

Combine like terms: 4 + -4 = 0
0 + x = -0.816496583 + -4
x = -0.816496583 + -4

Combine like terms: -0.816496583 + -4 = -4.816496583
x = -4.816496583

Simplifying
x = -4.816496583


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.183503417, -4.816496583}
Solution
x = {-3.183503417, -4.816496583}

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