42x^2+273x+112=0

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Solution for 42x^2+273x+112=0 equation: 


Simplifying
42x2 + 273x + 112 = 0

Reorder the terms:
112 + 273x + 42x2 = 0

Solving
112 + 273x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(16 + 39x + 6x2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(16 + 39x + 6x2)' equal to zero and attempt to solve:

Simplifying
16 + 39x + 6x2 = 0

Solving
16 + 39x + 6x2 = 0

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

Divide each side by '6'.
2.666666667 + 6.5x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + 6.5x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + 6.5x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + 6.5x + x2 = 0 + -2.666666667
6.5x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
6.5x + x2 = -2.666666667

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = -2.666666667 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = -2.666666667 + 10.5625

Combine like terms: -2.666666667 + 10.5625 = 7.895833333
10.5625 + 6.5x + x2 = 7.895833333

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 7.895833333

Calculate the square root of the right side: 2.80995255

Break this problem into two subproblems by setting 
(x + 3.25) equal to 2.80995255 and -2.80995255.


Subproblem 1
x + 3.25 = 2.80995255

Simplifying
x + 3.25 = 2.80995255

Reorder the terms:
3.25 + x = 2.80995255

Solving
3.25 + x = 2.80995255

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = 2.80995255 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 2.80995255 + -3.25
x = 2.80995255 + -3.25

Combine like terms: 2.80995255 + -3.25 = -0.44004745
x = -0.44004745

Simplifying
x = -0.44004745


Subproblem 2
x + 3.25 = -2.80995255

Simplifying
x + 3.25 = -2.80995255

Reorder the terms:
3.25 + x = -2.80995255

Solving
3.25 + x = -2.80995255

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = -2.80995255 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -2.80995255 + -3.25
x = -2.80995255 + -3.25

Combine like terms: -2.80995255 + -3.25 = -6.05995255
x = -6.05995255

Simplifying
x = -6.05995255


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.44004745, -6.05995255}
Solution
x = {-0.44004745, -6.05995255}

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