3x^2+13x-46=0

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Solution for 3x^2+13x-46=0 equation: 


Simplifying
3x2 + 13x + -46 = 0

Reorder the terms:
-46 + 13x + 3x2 = 0

Solving
-46 + 13x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-15.33333333 + 4.333333333x + x2 = 0

Move the constant term to the right:

Add '15.33333333' to each side of the equation.
-15.33333333 + 4.333333333x + 15.33333333 + x2 = 0 + 15.33333333

Reorder the terms:
-15.33333333 + 15.33333333 + 4.333333333x + x2 = 0 + 15.33333333

Combine like terms: -15.33333333 + 15.33333333 = 0.00000000
0.00000000 + 4.333333333x + x2 = 0 + 15.33333333
4.333333333x + x2 = 0 + 15.33333333

Combine like terms: 0 + 15.33333333 = 15.33333333
4.333333333x + x2 = 15.33333333

The x term is 4.333333333x.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333x + 4.694444446 + x2 = 15.33333333 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333x + x2 = 15.33333333 + 4.694444446

Combine like terms: 15.33333333 + 4.694444446 = 20.027777776
4.694444446 + 4.333333333x + x2 = 20.027777776

Factor a perfect square on the left side:
(x + 2.166666667)(x + 2.166666667) = 20.027777776

Calculate the square root of the right side: 4.475240527

Break this problem into two subproblems by setting 
(x + 2.166666667) equal to 4.475240527 and -4.475240527.


Subproblem 1
x + 2.166666667 = 4.475240527

Simplifying
x + 2.166666667 = 4.475240527

Reorder the terms:
2.166666667 + x = 4.475240527

Solving
2.166666667 + x = 4.475240527

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = 4.475240527 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = 4.475240527 + -2.166666667
x = 4.475240527 + -2.166666667

Combine like terms: 4.475240527 + -2.166666667 = 2.30857386
x = 2.30857386

Simplifying
x = 2.30857386


Subproblem 2
x + 2.166666667 = -4.475240527

Simplifying
x + 2.166666667 = -4.475240527

Reorder the terms:
2.166666667 + x = -4.475240527

Solving
2.166666667 + x = -4.475240527

Solving for variable 'x'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + x = -4.475240527 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + x = -4.475240527 + -2.166666667
x = -4.475240527 + -2.166666667

Combine like terms: -4.475240527 + -2.166666667 = -6.641907194
x = -6.641907194

Simplifying
x = -6.641907194


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.30857386, -6.641907194}

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