-3x^2-42x-145=0

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Solution for -3x^2-42x-145=0 equation: 


Simplifying
-3x2 + -42x + -145 = 0

Reorder the terms:
-145 + -42x + -3x2 = 0

Solving
-145 + -42x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(145 + 42x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(145 + 42x + 3x2)' equal to zero and attempt to solve:

Simplifying
145 + 42x + 3x2 = 0

Solving
145 + 42x + 3x2 = 0

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

Divide each side by '3'.
48.33333333 + 14x + x2 = 0

Move the constant term to the right:

Add '-48.33333333' to each side of the equation.
48.33333333 + 14x + -48.33333333 + x2 = 0 + -48.33333333

Reorder the terms:
48.33333333 + -48.33333333 + 14x + x2 = 0 + -48.33333333

Combine like terms: 48.33333333 + -48.33333333 = 0.00000000
0.00000000 + 14x + x2 = 0 + -48.33333333
14x + x2 = 0 + -48.33333333

Combine like terms: 0 + -48.33333333 = -48.33333333
14x + x2 = -48.33333333

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -48.33333333 + 49

Reorder the terms:
49 + 14x + x2 = -48.33333333 + 49

Combine like terms: -48.33333333 + 49 = 0.66666667
49 + 14x + x2 = 0.66666667

Factor a perfect square on the left side:
(x + 7)(x + 7) = 0.66666667

Calculate the square root of the right side: 0.816496583

Break this problem into two subproblems by setting 
(x + 7) equal to 0.816496583 and -0.816496583.


Subproblem 1
x + 7 = 0.816496583

Simplifying
x + 7 = 0.816496583

Reorder the terms:
7 + x = 0.816496583

Solving
7 + x = 0.816496583

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 0.816496583 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0.816496583 + -7
x = 0.816496583 + -7

Combine like terms: 0.816496583 + -7 = -6.183503417
x = -6.183503417

Simplifying
x = -6.183503417


Subproblem 2
x + 7 = -0.816496583

Simplifying
x + 7 = -0.816496583

Reorder the terms:
7 + x = -0.816496583

Solving
7 + x = -0.816496583

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -0.816496583 + -7

Combine like terms: 7 + -7 = 0
0 + x = -0.816496583 + -7
x = -0.816496583 + -7

Combine like terms: -0.816496583 + -7 = -7.816496583
x = -7.816496583

Simplifying
x = -7.816496583


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-6.183503417, -7.816496583}
Solution
x = {-6.183503417, -7.816496583}

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