3x^2-21x+10=0

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Solution for 3x^2-21x+10=0 equation: 


Simplifying
3x2 + -21x + 10 = 0

Reorder the terms:
10 + -21x + 3x2 = 0

Solving
10 + -21x + 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'.
3.333333333 + -7x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -7x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -7x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -7x + x2 = 0 + -3.333333333
-7x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-7x + x2 = -3.333333333

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -3.333333333 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -3.333333333 + 12.25

Combine like terms: -3.333333333 + 12.25 = 8.916666667
12.25 + -7x + x2 = 8.916666667

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 8.916666667

Calculate the square root of the right side: 2.986078811

Break this problem into two subproblems by setting 
(x + -3.5) equal to 2.986078811 and -2.986078811.


Subproblem 1
x + -3.5 = 2.986078811

Simplifying
x + -3.5 = 2.986078811

Reorder the terms:
-3.5 + x = 2.986078811

Solving
-3.5 + x = 2.986078811

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 2.986078811 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 2.986078811 + 3.5
x = 2.986078811 + 3.5

Combine like terms: 2.986078811 + 3.5 = 6.486078811
x = 6.486078811

Simplifying
x = 6.486078811


Subproblem 2
x + -3.5 = -2.986078811

Simplifying
x + -3.5 = -2.986078811

Reorder the terms:
-3.5 + x = -2.986078811

Solving
-3.5 + x = -2.986078811

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -2.986078811 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -2.986078811 + 3.5
x = -2.986078811 + 3.5

Combine like terms: -2.986078811 + 3.5 = 0.513921189
x = 0.513921189

Simplifying
x = 0.513921189


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.486078811, 0.513921189}

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