t^2-10t+14=0

Solution for t^2-10t+14=0 equation:

Simplifying
t2 + -10t + 14 = 0

Reorder the terms:
14 + -10t + t2 = 0

Solving
14 + -10t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -10t + -14 + t2 = 0 + -14

Reorder the terms:
14 + -14 + -10t + t2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -10t + t2 = 0 + -14
-10t + t2 = 0 + -14

Combine like terms: 0 + -14 = -14
-10t + t2 = -14

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

Add '25' to each side of the equation.
-10t + 25 + t2 = -14 + 25

Reorder the terms:
25 + -10t + t2 = -14 + 25

Combine like terms: -14 + 25 = 11
25 + -10t + t2 = 11

Factor a perfect square on the left side:
(t + -5)(t + -5) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(t + -5) equal to 3.31662479 and -3.31662479.

Subproblem 1
t + -5 = 3.31662479

Simplifying
t + -5 = 3.31662479

Reorder the terms:
-5 + t = 3.31662479

Solving
-5 + t = 3.31662479

Solving for variable 't'.

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

Add '5' to each side of the equation.
-5 + 5 + t = 3.31662479 + 5

Combine like terms: -5 + 5 = 0
0 + t = 3.31662479 + 5
t = 3.31662479 + 5

Combine like terms: 3.31662479 + 5 = 8.31662479
t = 8.31662479

Simplifying
t = 8.31662479

Subproblem 2
t + -5 = -3.31662479

Simplifying
t + -5 = -3.31662479

Reorder the terms:
-5 + t = -3.31662479

Solving
-5 + t = -3.31662479

Solving for variable 't'.

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

Add '5' to each side of the equation.
-5 + 5 + t = -3.31662479 + 5

Combine like terms: -5 + 5 = 0
0 + t = -3.31662479 + 5
t = -3.31662479 + 5

Combine like terms: -3.31662479 + 5 = 1.68337521
t = 1.68337521

Simplifying
t = 1.68337521

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.31662479, 1.68337521}