3x^2+8x-5=20

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Solution for 3x^2+8x-5=20 equation: 


Simplifying
3x2 + 8x + -5 = 20

Reorder the terms:
-5 + 8x + 3x2 = 20

Solving
-5 + 8x + 3x2 = 20

Solving for variable 'x'.

Reorder the terms:
-5 + -20 + 8x + 3x2 = 20 + -20

Combine like terms: -5 + -20 = -25
-25 + 8x + 3x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-25 + 8x + 3x2 = 0

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

Divide each side by '3'.
-8.333333333 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '8.333333333' to each side of the equation.
-8.333333333 + 2.666666667x + 8.333333333 + x2 = 0 + 8.333333333

Reorder the terms:
-8.333333333 + 8.333333333 + 2.666666667x + x2 = 0 + 8.333333333

Combine like terms: -8.333333333 + 8.333333333 = 0.000000000
0.000000000 + 2.666666667x + x2 = 0 + 8.333333333
2.666666667x + x2 = 0 + 8.333333333

Combine like terms: 0 + 8.333333333 = 8.333333333
2.666666667x + x2 = 8.333333333

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 = 8.333333333 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 8.333333333 + 1.777777780

Combine like terms: 8.333333333 + 1.777777780 = 10.111111113
1.777777780 + 2.666666667x + x2 = 10.111111113

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 10.111111113

Calculate the square root of the right side: 3.179797338

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 3.179797338 and -3.179797338.


Subproblem 1
x + 1.333333334 = 3.179797338

Simplifying
x + 1.333333334 = 3.179797338

Reorder the terms:
1.333333334 + x = 3.179797338

Solving
1.333333334 + x = 3.179797338

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 = 3.179797338 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = 3.179797338 + -1.333333334
x = 3.179797338 + -1.333333334

Combine like terms: 3.179797338 + -1.333333334 = 1.846464004
x = 1.846464004

Simplifying
x = 1.846464004


Subproblem 2
x + 1.333333334 = -3.179797338

Simplifying
x + 1.333333334 = -3.179797338

Reorder the terms:
1.333333334 + x = -3.179797338

Solving
1.333333334 + x = -3.179797338

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 = -3.179797338 + -1.333333334

Combine like terms: 1.333333334 + -1.333333334 = 0.000000000
0.000000000 + x = -3.179797338 + -1.333333334
x = -3.179797338 + -1.333333334

Combine like terms: -3.179797338 + -1.333333334 = -4.513130672
x = -4.513130672

Simplifying
x = -4.513130672


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.846464004, -4.513130672}

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