3x^2-25x+16=0

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Solution for 3x^2-25x+16=0 equation: 


Simplifying
3x2 + -25x + 16 = 0

Reorder the terms:
16 + -25x + 3x2 = 0

Solving
16 + -25x + 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'.
5.333333333 + -8.333333333x + x2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + -8.333333333x + -5.333333333 + x2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + -8.333333333x + x2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + -8.333333333x + x2 = 0 + -5.333333333
-8.333333333x + x2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
-8.333333333x + x2 = -5.333333333

The x term is -8.333333333x.  Take half its coefficient (-4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
-8.333333333x + 17.36111111 + x2 = -5.333333333 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333x + x2 = -5.333333333 + 17.36111111

Combine like terms: -5.333333333 + 17.36111111 = 12.027777777
17.36111111 + -8.333333333x + x2 = 12.027777777

Factor a perfect square on the left side:
(x + -4.166666667)(x + -4.166666667) = 12.027777777

Calculate the square root of the right side: 3.468108674

Break this problem into two subproblems by setting 
(x + -4.166666667) equal to 3.468108674 and -3.468108674.


Subproblem 1
x + -4.166666667 = 3.468108674

Simplifying
x + -4.166666667 = 3.468108674

Reorder the terms:
-4.166666667 + x = 3.468108674

Solving
-4.166666667 + x = 3.468108674

Solving for variable 'x'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + x = 3.468108674 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = 3.468108674 + 4.166666667
x = 3.468108674 + 4.166666667

Combine like terms: 3.468108674 + 4.166666667 = 7.634775341
x = 7.634775341

Simplifying
x = 7.634775341


Subproblem 2
x + -4.166666667 = -3.468108674

Simplifying
x + -4.166666667 = -3.468108674

Reorder the terms:
-4.166666667 + x = -3.468108674

Solving
-4.166666667 + x = -3.468108674

Solving for variable 'x'.

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

Add '4.166666667' to each side of the equation.
-4.166666667 + 4.166666667 + x = -3.468108674 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + x = -3.468108674 + 4.166666667
x = -3.468108674 + 4.166666667

Combine like terms: -3.468108674 + 4.166666667 = 0.698557993
x = 0.698557993

Simplifying
x = 0.698557993


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.634775341, 0.698557993}

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