3x^2-30x+62=0

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Solution for 3x^2-30x+62=0 equation: 


Simplifying
3x2 + -30x + 62 = 0

Reorder the terms:
62 + -30x + 3x2 = 0

Solving
62 + -30x + 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'.
20.66666667 + -10x + x2 = 0

Move the constant term to the right:

Add '-20.66666667' to each side of the equation.
20.66666667 + -10x + -20.66666667 + x2 = 0 + -20.66666667

Reorder the terms:
20.66666667 + -20.66666667 + -10x + x2 = 0 + -20.66666667

Combine like terms: 20.66666667 + -20.66666667 = 0.00000000
0.00000000 + -10x + x2 = 0 + -20.66666667
-10x + x2 = 0 + -20.66666667

Combine like terms: 0 + -20.66666667 = -20.66666667
-10x + x2 = -20.66666667

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -20.66666667 + 25

Reorder the terms:
25 + -10x + x2 = -20.66666667 + 25

Combine like terms: -20.66666667 + 25 = 4.33333333
25 + -10x + x2 = 4.33333333

Factor a perfect square on the left side:
(x + -5)(x + -5) = 4.33333333

Calculate the square root of the right side: 2.081665999

Break this problem into two subproblems by setting 
(x + -5) equal to 2.081665999 and -2.081665999.


Subproblem 1
x + -5 = 2.081665999

Simplifying
x + -5 = 2.081665999

Reorder the terms:
-5 + x = 2.081665999

Solving
-5 + x = 2.081665999

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 2.081665999 + 5

Combine like terms: -5 + 5 = 0
0 + x = 2.081665999 + 5
x = 2.081665999 + 5

Combine like terms: 2.081665999 + 5 = 7.081665999
x = 7.081665999

Simplifying
x = 7.081665999


Subproblem 2
x + -5 = -2.081665999

Simplifying
x + -5 = -2.081665999

Reorder the terms:
-5 + x = -2.081665999

Solving
-5 + x = -2.081665999

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -2.081665999 + 5

Combine like terms: -5 + 5 = 0
0 + x = -2.081665999 + 5
x = -2.081665999 + 5

Combine like terms: -2.081665999 + 5 = 2.918334001
x = 2.918334001

Simplifying
x = 2.918334001


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.081665999, 2.918334001}

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