3x^2+20x-68=0

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Solution for 3x^2+20x-68=0 equation: 


Simplifying
3x2 + 20x + -68 = 0

Reorder the terms:
-68 + 20x + 3x2 = 0

Solving
-68 + 20x + 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'.
-22.66666667 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '22.66666667' to each side of the equation.
-22.66666667 + 6.666666667x + 22.66666667 + x2 = 0 + 22.66666667

Reorder the terms:
-22.66666667 + 22.66666667 + 6.666666667x + x2 = 0 + 22.66666667

Combine like terms: -22.66666667 + 22.66666667 = 0.00000000
0.00000000 + 6.666666667x + x2 = 0 + 22.66666667
6.666666667x + x2 = 0 + 22.66666667

Combine like terms: 0 + 22.66666667 = 22.66666667
6.666666667x + x2 = 22.66666667

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = 22.66666667 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 22.66666667 + 11.11111112

Combine like terms: 22.66666667 + 11.11111112 = 33.77777779
11.11111112 + 6.666666667x + x2 = 33.77777779

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 33.77777779

Calculate the square root of the right side: 5.811865259

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 5.811865259 and -5.811865259.


Subproblem 1
x + 3.333333334 = 5.811865259

Simplifying
x + 3.333333334 = 5.811865259

Reorder the terms:
3.333333334 + x = 5.811865259

Solving
3.333333334 + x = 5.811865259

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 5.811865259 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 5.811865259 + -3.333333334
x = 5.811865259 + -3.333333334

Combine like terms: 5.811865259 + -3.333333334 = 2.478531925
x = 2.478531925

Simplifying
x = 2.478531925


Subproblem 2
x + 3.333333334 = -5.811865259

Simplifying
x + 3.333333334 = -5.811865259

Reorder the terms:
3.333333334 + x = -5.811865259

Solving
3.333333334 + x = -5.811865259

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -5.811865259 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -5.811865259 + -3.333333334
x = -5.811865259 + -3.333333334

Combine like terms: -5.811865259 + -3.333333334 = -9.145198593
x = -9.145198593

Simplifying
x = -9.145198593


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.478531925, -9.145198593}

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