3x^2-20x-75=0

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Solution for 3x^2-20x-75=0 equation: 


Simplifying
3x2 + -20x + -75 = 0

Reorder the terms:
-75 + -20x + 3x2 = 0

Solving
-75 + -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'.
-25 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -6.666666667x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -6.666666667x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -6.666666667x + x2 = 0 + 25
-6.666666667x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-6.666666667x + x2 = 25

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 = 25 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = 25 + 11.11111112

Combine like terms: 25 + 11.11111112 = 36.11111112
11.11111112 + -6.666666667x + x2 = 36.11111112

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 36.11111112

Calculate the square root of the right side: 6.009252127

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 6.009252127 and -6.009252127.


Subproblem 1
x + -3.333333334 = 6.009252127

Simplifying
x + -3.333333334 = 6.009252127

Reorder the terms:
-3.333333334 + x = 6.009252127

Solving
-3.333333334 + x = 6.009252127

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 = 6.009252127 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 6.009252127 + 3.333333334
x = 6.009252127 + 3.333333334

Combine like terms: 6.009252127 + 3.333333334 = 9.342585461
x = 9.342585461

Simplifying
x = 9.342585461


Subproblem 2
x + -3.333333334 = -6.009252127

Simplifying
x + -3.333333334 = -6.009252127

Reorder the terms:
-3.333333334 + x = -6.009252127

Solving
-3.333333334 + x = -6.009252127

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 = -6.009252127 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -6.009252127 + 3.333333334
x = -6.009252127 + 3.333333334

Combine like terms: -6.009252127 + 3.333333334 = -2.675918793
x = -2.675918793

Simplifying
x = -2.675918793


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.342585461, -2.675918793}

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