12x^2+42x+20=0

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Solution for 12x^2+42x+20=0 equation:


Simplifying
12x2 + 42x + 20 = 0

Reorder the terms:
20 + 42x + 12x2 = 0

Solving
20 + 42x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + 21x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + 21x + 6x2)' equal to zero and attempt to solve:

Simplifying
10 + 21x + 6x2 = 0

Solving
10 + 21x + 6x2 = 0

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

Divide each side by '6'.
1.666666667 + 3.5x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 3.5x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 3.5x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 3.5x + x2 = 0 + -1.666666667
3.5x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
3.5x + x2 = -1.666666667

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = -1.666666667 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = -1.666666667 + 3.0625

Combine like terms: -1.666666667 + 3.0625 = 1.395833333
3.0625 + 3.5x + x2 = 1.395833333

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 1.395833333

Calculate the square root of the right side: 1.181453906

Break this problem into two subproblems by setting 
(x + 1.75) equal to 1.181453906 and -1.181453906.


Subproblem 1
x + 1.75 = 1.181453906

Simplifying
x + 1.75 = 1.181453906

Reorder the terms:
1.75 + x = 1.181453906

Solving
1.75 + x = 1.181453906

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 1.181453906 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 1.181453906 + -1.75
x = 1.181453906 + -1.75

Combine like terms: 1.181453906 + -1.75 = -0.568546094
x = -0.568546094

Simplifying
x = -0.568546094


Subproblem 2
x + 1.75 = -1.181453906

Simplifying
x + 1.75 = -1.181453906

Reorder the terms:
1.75 + x = -1.181453906

Solving
1.75 + x = -1.181453906

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -1.181453906 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -1.181453906 + -1.75
x = -1.181453906 + -1.75

Combine like terms: -1.181453906 + -1.75 = -2.931453906
x = -2.931453906

Simplifying
x = -2.931453906


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.568546094, -2.931453906}
Solution
x = {-0.568546094, -2.931453906}

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