3x^2-70x+280=0

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Solution for 3x^2-70x+280=0 equation: 


Simplifying
3x2 + -70x + 280 = 0

Reorder the terms:
280 + -70x + 3x2 = 0

Solving
280 + -70x + 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'.
93.33333333 + -23.33333333x + x2 = 0

Move the constant term to the right:

Add '-93.33333333' to each side of the equation.
93.33333333 + -23.33333333x + -93.33333333 + x2 = 0 + -93.33333333

Reorder the terms:
93.33333333 + -93.33333333 + -23.33333333x + x2 = 0 + -93.33333333

Combine like terms: 93.33333333 + -93.33333333 = 0.00000000
0.00000000 + -23.33333333x + x2 = 0 + -93.33333333
-23.33333333x + x2 = 0 + -93.33333333

Combine like terms: 0 + -93.33333333 = -93.33333333
-23.33333333x + x2 = -93.33333333

The x term is -23.33333333x.  Take half its coefficient (-11.66666667).
Square it (136.1111112) and add it to both sides.

Add '136.1111112' to each side of the equation.
-23.33333333x + 136.1111112 + x2 = -93.33333333 + 136.1111112

Reorder the terms:
136.1111112 + -23.33333333x + x2 = -93.33333333 + 136.1111112

Combine like terms: -93.33333333 + 136.1111112 = 42.77777787
136.1111112 + -23.33333333x + x2 = 42.77777787

Factor a perfect square on the left side:
(x + -11.66666667)(x + -11.66666667) = 42.77777787

Calculate the square root of the right side: 6.540472297

Break this problem into two subproblems by setting 
(x + -11.66666667) equal to 6.540472297 and -6.540472297.


Subproblem 1
x + -11.66666667 = 6.540472297

Simplifying
x + -11.66666667 = 6.540472297

Reorder the terms:
-11.66666667 + x = 6.540472297

Solving
-11.66666667 + x = 6.540472297

Solving for variable 'x'.

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

Add '11.66666667' to each side of the equation.
-11.66666667 + 11.66666667 + x = 6.540472297 + 11.66666667

Combine like terms: -11.66666667 + 11.66666667 = 0.00000000
0.00000000 + x = 6.540472297 + 11.66666667
x = 6.540472297 + 11.66666667

Combine like terms: 6.540472297 + 11.66666667 = 18.207138967
x = 18.207138967

Simplifying
x = 18.207138967


Subproblem 2
x + -11.66666667 = -6.540472297

Simplifying
x + -11.66666667 = -6.540472297

Reorder the terms:
-11.66666667 + x = -6.540472297

Solving
-11.66666667 + x = -6.540472297

Solving for variable 'x'.

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

Add '11.66666667' to each side of the equation.
-11.66666667 + 11.66666667 + x = -6.540472297 + 11.66666667

Combine like terms: -11.66666667 + 11.66666667 = 0.00000000
0.00000000 + x = -6.540472297 + 11.66666667
x = -6.540472297 + 11.66666667

Combine like terms: -6.540472297 + 11.66666667 = 5.126194373
x = 5.126194373

Simplifying
x = 5.126194373


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.207138967, 5.126194373}

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