3x^2+5x-2=12

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Solution for 3x^2+5x-2=12 equation: 


Simplifying
3x2 + 5x + -2 = 12

Reorder the terms:
-2 + 5x + 3x2 = 12

Solving
-2 + 5x + 3x2 = 12

Solving for variable 'x'.

Reorder the terms:
-2 + -12 + 5x + 3x2 = 12 + -12

Combine like terms: -2 + -12 = -14
-14 + 5x + 3x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-14 + 5x + 3x2 = 0

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

Divide each side by '3'.
-4.666666667 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + 1.666666667x + 4.666666667 + x2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + 1.666666667x + x2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + 4.666666667
1.666666667x + x2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
1.666666667x + x2 = 4.666666667

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 4.666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 4.666666667 + 0.6944444447

Combine like terms: 4.666666667 + 0.6944444447 = 5.3611111117
0.6944444447 + 1.666666667x + x2 = 5.3611111117

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 5.3611111117

Calculate the square root of the right side: 2.315407332

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 2.315407332 and -2.315407332.


Subproblem 1
x + 0.8333333335 = 2.315407332

Simplifying
x + 0.8333333335 = 2.315407332

Reorder the terms:
0.8333333335 + x = 2.315407332

Solving
0.8333333335 + x = 2.315407332

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 2.315407332 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 2.315407332 + -0.8333333335
x = 2.315407332 + -0.8333333335

Combine like terms: 2.315407332 + -0.8333333335 = 1.4820739985
x = 1.4820739985

Simplifying
x = 1.4820739985


Subproblem 2
x + 0.8333333335 = -2.315407332

Simplifying
x + 0.8333333335 = -2.315407332

Reorder the terms:
0.8333333335 + x = -2.315407332

Solving
0.8333333335 + x = -2.315407332

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -2.315407332 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -2.315407332 + -0.8333333335
x = -2.315407332 + -0.8333333335

Combine like terms: -2.315407332 + -0.8333333335 = -3.1487406655
x = -3.1487406655

Simplifying
x = -3.1487406655


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4820739985, -3.1487406655}

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