3x^2-13x-42=0

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Solution for 3x^2-13x-42=0 equation: 


Simplifying
3x2 + -13x + -42 = 0

Reorder the terms:
-42 + -13x + 3x2 = 0

Solving
-42 + -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'.
-14 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -4.333333333x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -4.333333333x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -4.333333333x + x2 = 0 + 14
-4.333333333x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-4.333333333x + x2 = 14

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 = 14 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = 14 + 4.694444446

Combine like terms: 14 + 4.694444446 = 18.694444446
4.694444446 + -4.333333333x + x2 = 18.694444446

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 18.694444446

Calculate the square root of the right side: 4.323707257

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 4.323707257 and -4.323707257.


Subproblem 1
x + -2.166666667 = 4.323707257

Simplifying
x + -2.166666667 = 4.323707257

Reorder the terms:
-2.166666667 + x = 4.323707257

Solving
-2.166666667 + x = 4.323707257

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 = 4.323707257 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = 4.323707257 + 2.166666667
x = 4.323707257 + 2.166666667

Combine like terms: 4.323707257 + 2.166666667 = 6.490373924
x = 6.490373924

Simplifying
x = 6.490373924


Subproblem 2
x + -2.166666667 = -4.323707257

Simplifying
x + -2.166666667 = -4.323707257

Reorder the terms:
-2.166666667 + x = -4.323707257

Solving
-2.166666667 + x = -4.323707257

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 = -4.323707257 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = -4.323707257 + 2.166666667
x = -4.323707257 + 2.166666667

Combine like terms: -4.323707257 + 2.166666667 = -2.15704059
x = -2.15704059

Simplifying
x = -2.15704059


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.490373924, -2.15704059}

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