12x^2+24x+1.04=0

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Solution for 12x^2+24x+1.04=0 equation:


Simplifying
12x2 + 24x + 1.04 = 0

Reorder the terms:
1.04 + 24x + 12x2 = 0

Solving
1.04 + 24x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
0.08666666667 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.08666666667' to each side of the equation.
0.08666666667 + 2x + -0.08666666667 + x2 = 0 + -0.08666666667

Reorder the terms:
0.08666666667 + -0.08666666667 + 2x + x2 = 0 + -0.08666666667

Combine like terms: 0.08666666667 + -0.08666666667 = 0.00000000000
0.00000000000 + 2x + x2 = 0 + -0.08666666667
2x + x2 = 0 + -0.08666666667

Combine like terms: 0 + -0.08666666667 = -0.08666666667
2x + x2 = -0.08666666667

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.08666666667 + 1

Reorder the terms:
1 + 2x + x2 = -0.08666666667 + 1

Combine like terms: -0.08666666667 + 1 = 0.91333333333
1 + 2x + x2 = 0.91333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.91333333333

Calculate the square root of the right side: 0.955684746

Break this problem into two subproblems by setting 
(x + 1) equal to 0.955684746 and -0.955684746.

Subproblem 1

x + 1 = 0.955684746 Simplifying x + 1 = 0.955684746 Reorder the terms: 1 + x = 0.955684746 Solving 1 + x = 0.955684746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.955684746 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.955684746 + -1 x = 0.955684746 + -1 Combine like terms: 0.955684746 + -1 = -0.044315254 x = -0.044315254 Simplifying x = -0.044315254

Subproblem 2

x + 1 = -0.955684746 Simplifying x + 1 = -0.955684746 Reorder the terms: 1 + x = -0.955684746 Solving 1 + x = -0.955684746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.955684746 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.955684746 + -1 x = -0.955684746 + -1 Combine like terms: -0.955684746 + -1 = -1.955684746 x = -1.955684746 Simplifying x = -1.955684746

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.044315254, -1.955684746}

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