3x^2-65x+150=0

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Solution for 3x^2-65x+150=0 equation: 


Simplifying
3x2 + -65x + 150 = 0

Reorder the terms:
150 + -65x + 3x2 = 0

Solving
150 + -65x + 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'.
50 + -21.66666667x + x2 = 0

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + -21.66666667x + -50 + x2 = 0 + -50

Reorder the terms:
50 + -50 + -21.66666667x + x2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -21.66666667x + x2 = 0 + -50
-21.66666667x + x2 = 0 + -50

Combine like terms: 0 + -50 = -50
-21.66666667x + x2 = -50

The x term is -21.66666667x.  Take half its coefficient (-10.83333334).
Square it (117.3611113) and add it to both sides.

Add '117.3611113' to each side of the equation.
-21.66666667x + 117.3611113 + x2 = -50 + 117.3611113

Reorder the terms:
117.3611113 + -21.66666667x + x2 = -50 + 117.3611113

Combine like terms: -50 + 117.3611113 = 67.3611113
117.3611113 + -21.66666667x + x2 = 67.3611113

Factor a perfect square on the left side:
(x + -10.83333334)(x + -10.83333334) = 67.3611113

Calculate the square root of the right side: 8.207381513

Break this problem into two subproblems by setting 
(x + -10.83333334) equal to 8.207381513 and -8.207381513.


Subproblem 1
x + -10.83333334 = 8.207381513

Simplifying
x + -10.83333334 = 8.207381513

Reorder the terms:
-10.83333334 + x = 8.207381513

Solving
-10.83333334 + x = 8.207381513

Solving for variable 'x'.

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

Add '10.83333334' to each side of the equation.
-10.83333334 + 10.83333334 + x = 8.207381513 + 10.83333334

Combine like terms: -10.83333334 + 10.83333334 = 0.00000000
0.00000000 + x = 8.207381513 + 10.83333334
x = 8.207381513 + 10.83333334

Combine like terms: 8.207381513 + 10.83333334 = 19.040714853
x = 19.040714853

Simplifying
x = 19.040714853


Subproblem 2
x + -10.83333334 = -8.207381513

Simplifying
x + -10.83333334 = -8.207381513

Reorder the terms:
-10.83333334 + x = -8.207381513

Solving
-10.83333334 + x = -8.207381513

Solving for variable 'x'.

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

Add '10.83333334' to each side of the equation.
-10.83333334 + 10.83333334 + x = -8.207381513 + 10.83333334

Combine like terms: -10.83333334 + 10.83333334 = 0.00000000
0.00000000 + x = -8.207381513 + 10.83333334
x = -8.207381513 + 10.83333334

Combine like terms: -8.207381513 + 10.83333334 = 2.625951827
x = 2.625951827

Simplifying
x = 2.625951827


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.040714853, 2.625951827}

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