12x^2+3x=8

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Solution for 12x^2+3x=8 equation:


Simplifying
12x2 + 3x = 8

Reorder the terms:
3x + 12x2 = 8

Solving
3x + 12x2 = 8

Solving for variable 'x'.

Reorder the terms:
-8 + 3x + 12x2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 3x + 12x2 = 0

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

Divide each side by '12'.
-0.6666666667 + 0.25x + x2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + 0.25x + 0.6666666667 + x2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + 0.25x + x2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + 0.25x + x2 = 0 + 0.6666666667
0.25x + x2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
0.25x + x2 = 0.6666666667

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = 0.6666666667 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 0.6666666667 + 0.015625

Combine like terms: 0.6666666667 + 0.015625 = 0.6822916667
0.015625 + 0.25x + x2 = 0.6822916667

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 0.6822916667

Calculate the square root of the right side: 0.826009483

Break this problem into two subproblems by setting 
(x + 0.125) equal to 0.826009483 and -0.826009483.

Subproblem 1

x + 0.125 = 0.826009483 Simplifying x + 0.125 = 0.826009483 Reorder the terms: 0.125 + x = 0.826009483 Solving 0.125 + x = 0.826009483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.826009483 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.826009483 + -0.125 x = 0.826009483 + -0.125 Combine like terms: 0.826009483 + -0.125 = 0.701009483 x = 0.701009483 Simplifying x = 0.701009483

Subproblem 2

x + 0.125 = -0.826009483 Simplifying x + 0.125 = -0.826009483 Reorder the terms: 0.125 + x = -0.826009483 Solving 0.125 + x = -0.826009483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.826009483 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.826009483 + -0.125 x = -0.826009483 + -0.125 Combine like terms: -0.826009483 + -0.125 = -0.951009483 x = -0.951009483 Simplifying x = -0.951009483

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.701009483, -0.951009483}

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