3x^2+5x-13=12

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Solution for 3x^2+5x-13=12 equation: 


Simplifying
3x2 + 5x + -13 = 12

Reorder the terms:
-13 + 5x + 3x2 = 12

Solving
-13 + 5x + 3x2 = 12

Solving for variable 'x'.

Reorder the terms:
-13 + -12 + 5x + 3x2 = 12 + -12

Combine like terms: -13 + -12 = -25
-25 + 5x + 3x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-25 + 5x + 3x2 = 0

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

Divide each side by '3'.
-8.333333333 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + 1.666666667x + 8.333333333 + x2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + 1.666666667x + x2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + 8.333333333
1.666666667x + x2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
1.666666667x + x2 = 8.333333333

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 = 8.333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 8.333333333 + 0.6944444447

Combine like terms: 8.333333333 + 0.6944444447 = 9.0277777777
0.6944444447 + 1.666666667x + x2 = 9.0277777777

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 9.0277777777

Calculate the square root of the right side: 3.004626063

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 3.004626063 and -3.004626063.


Subproblem 1
x + 0.8333333335 = 3.004626063

Simplifying
x + 0.8333333335 = 3.004626063

Reorder the terms:
0.8333333335 + x = 3.004626063

Solving
0.8333333335 + x = 3.004626063

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 = 3.004626063 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 3.004626063 + -0.8333333335
x = 3.004626063 + -0.8333333335

Combine like terms: 3.004626063 + -0.8333333335 = 2.1712927295
x = 2.1712927295

Simplifying
x = 2.1712927295


Subproblem 2
x + 0.8333333335 = -3.004626063

Simplifying
x + 0.8333333335 = -3.004626063

Reorder the terms:
0.8333333335 + x = -3.004626063

Solving
0.8333333335 + x = -3.004626063

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 = -3.004626063 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -3.004626063 + -0.8333333335
x = -3.004626063 + -0.8333333335

Combine like terms: -3.004626063 + -0.8333333335 = -3.8379593965
x = -3.8379593965

Simplifying
x = -3.8379593965


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.1712927295, -3.8379593965}

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