3x^2+24x+42=0

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Solution for 3x^2+24x+42=0 equation: 


Simplifying
3x2 + 24x + 42 = 0

Reorder the terms:
42 + 24x + 3x2 = 0

Solving
42 + 24x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + 8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(14 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
14 + 8x + x2 = 0

Solving
14 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + 8x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + 8x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + 8x + x2 = 0 + -14
8x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
8x + x2 = -14

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 = -14 + 16

Reorder the terms:
16 + 8x + x2 = -14 + 16

Combine like terms: -14 + 16 = 2
16 + 8x + x2 = 2

Factor a perfect square on the left side:
(x + 4)(x + 4) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + 4) equal to 1.414213562 and -1.414213562.


Subproblem 1
x + 4 = 1.414213562

Simplifying
x + 4 = 1.414213562

Reorder the terms:
4 + x = 1.414213562

Solving
4 + x = 1.414213562

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 = 1.414213562 + -4

Combine like terms: 4 + -4 = 0
0 + x = 1.414213562 + -4
x = 1.414213562 + -4

Combine like terms: 1.414213562 + -4 = -2.585786438
x = -2.585786438

Simplifying
x = -2.585786438


Subproblem 2
x + 4 = -1.414213562

Simplifying
x + 4 = -1.414213562

Reorder the terms:
4 + x = -1.414213562

Solving
4 + x = -1.414213562

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 = -1.414213562 + -4

Combine like terms: 4 + -4 = 0
0 + x = -1.414213562 + -4
x = -1.414213562 + -4

Combine like terms: -1.414213562 + -4 = -5.414213562
x = -5.414213562

Simplifying
x = -5.414213562


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.585786438, -5.414213562}
Solution
x = {-2.585786438, -5.414213562}

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