39x^2+55x+12=0

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Solution for 39x^2+55x+12=0 equation:


Simplifying
39x2 + 55x + 12 = 0

Reorder the terms:
12 + 55x + 39x2 = 0

Solving
12 + 55x + 39x2 = 0

Solving for variable 'x'.

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

Divide each side by '39'.
0.3076923077 + 1.41025641x + x2 = 0

Move the constant term to the right:

Add '-0.3076923077' to each side of the equation.
0.3076923077 + 1.41025641x + -0.3076923077 + x2 = 0 + -0.3076923077

Reorder the terms:
0.3076923077 + -0.3076923077 + 1.41025641x + x2 = 0 + -0.3076923077

Combine like terms: 0.3076923077 + -0.3076923077 = 0.0000000000
0.0000000000 + 1.41025641x + x2 = 0 + -0.3076923077
1.41025641x + x2 = 0 + -0.3076923077

Combine like terms: 0 + -0.3076923077 = -0.3076923077
1.41025641x + x2 = -0.3076923077

The x term is 1.41025641x.  Take half its coefficient (0.705128205).
Square it (0.4972057855) and add it to both sides.

Add '0.4972057855' to each side of the equation.
1.41025641x + 0.4972057855 + x2 = -0.3076923077 + 0.4972057855

Reorder the terms:
0.4972057855 + 1.41025641x + x2 = -0.3076923077 + 0.4972057855

Combine like terms: -0.3076923077 + 0.4972057855 = 0.1895134778
0.4972057855 + 1.41025641x + x2 = 0.1895134778

Factor a perfect square on the left side:
(x + 0.705128205)(x + 0.705128205) = 0.1895134778

Calculate the square root of the right side: 0.435331457

Break this problem into two subproblems by setting 
(x + 0.705128205) equal to 0.435331457 and -0.435331457.

Subproblem 1

x + 0.705128205 = 0.435331457 Simplifying x + 0.705128205 = 0.435331457 Reorder the terms: 0.705128205 + x = 0.435331457 Solving 0.705128205 + x = 0.435331457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.705128205' to each side of the equation. 0.705128205 + -0.705128205 + x = 0.435331457 + -0.705128205 Combine like terms: 0.705128205 + -0.705128205 = 0.000000000 0.000000000 + x = 0.435331457 + -0.705128205 x = 0.435331457 + -0.705128205 Combine like terms: 0.435331457 + -0.705128205 = -0.269796748 x = -0.269796748 Simplifying x = -0.269796748

Subproblem 2

x + 0.705128205 = -0.435331457 Simplifying x + 0.705128205 = -0.435331457 Reorder the terms: 0.705128205 + x = -0.435331457 Solving 0.705128205 + x = -0.435331457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.705128205' to each side of the equation. 0.705128205 + -0.705128205 + x = -0.435331457 + -0.705128205 Combine like terms: 0.705128205 + -0.705128205 = 0.000000000 0.000000000 + x = -0.435331457 + -0.705128205 x = -0.435331457 + -0.705128205 Combine like terms: -0.435331457 + -0.705128205 = -1.140459662 x = -1.140459662 Simplifying x = -1.140459662

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.269796748, -1.140459662}

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