3x^2+8x=20

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Solution for 3x^2+8x=20 equation: 


Simplifying
3x2 + 8x = 20

Reorder the terms:
8x + 3x2 = 20

Solving
8x + 3x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + 8x + 3x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 8x + 3x2 = 0

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

Divide each side by '3'.
-6.666666667 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + 2.666666667x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + 2.666666667x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + 2.666666667x + x2 = 0 + 6.666666667
2.666666667x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
2.666666667x + x2 = 6.666666667

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 6.666666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 6.666666667 + 1.777777780

Combine like terms: 6.666666667 + 1.777777780 = 8.444444447
1.777777780 + 2.666666667x + x2 = 8.444444447

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 8.444444447

Calculate the square root of the right side: 2.905932629

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 2.905932629 and -2.905932629.


Subproblem 1
x + 1.333333334 = 2.905932629

Simplifying
x + 1.333333334 = 2.905932629

Reorder the terms:
1.333333334 + x = 2.905932629

Solving
1.333333334 + x = 2.905932629

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = 2.905932629 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 2.905932629 + -1.333333334
x = 2.905932629 + -1.333333334

Combine like terms: 2.905932629 + -1.333333334 = 1.572599295
x = 1.572599295

Simplifying
x = 1.572599295


Subproblem 2
x + 1.333333334 = -2.905932629

Simplifying
x + 1.333333334 = -2.905932629

Reorder the terms:
1.333333334 + x = -2.905932629

Solving
1.333333334 + x = -2.905932629

Solving for variable 'x'.

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

Add '-1.333333334' to each side of the equation.
1.333333334 + -1.333333334 + x = -2.905932629 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -2.905932629 + -1.333333334
x = -2.905932629 + -1.333333334

Combine like terms: -2.905932629 + -1.333333334 = -4.239265963
x = -4.239265963

Simplifying
x = -4.239265963


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.572599295, -4.239265963}

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