3t^2-14t+10=0

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Solution for 3t^2-14t+10=0 equation: 


Simplifying
3t2 + -14t + 10 = 0

Reorder the terms:
10 + -14t + 3t2 = 0

Solving
10 + -14t + 3t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
3.333333333 + -4.666666667t + t2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -4.666666667t + -3.333333333 + t2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -4.666666667t + t2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -4.666666667t + t2 = 0 + -3.333333333
-4.666666667t + t2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-4.666666667t + t2 = -3.333333333

The t term is -4.666666667t.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667t + 5.444444448 + t2 = -3.333333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667t + t2 = -3.333333333 + 5.444444448

Combine like terms: -3.333333333 + 5.444444448 = 2.111111115
5.444444448 + -4.666666667t + t2 = 2.111111115

Factor a perfect square on the left side:
(t + -2.333333334)(t + -2.333333334) = 2.111111115

Calculate the square root of the right side: 1.452966316

Break this problem into two subproblems by setting 
(t + -2.333333334) equal to 1.452966316 and -1.452966316.


Subproblem 1
t + -2.333333334 = 1.452966316

Simplifying
t + -2.333333334 = 1.452966316

Reorder the terms:
-2.333333334 + t = 1.452966316

Solving
-2.333333334 + t = 1.452966316

Solving for variable 't'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + t = 1.452966316 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + t = 1.452966316 + 2.333333334
t = 1.452966316 + 2.333333334

Combine like terms: 1.452966316 + 2.333333334 = 3.78629965
t = 3.78629965

Simplifying
t = 3.78629965


Subproblem 2
t + -2.333333334 = -1.452966316

Simplifying
t + -2.333333334 = -1.452966316

Reorder the terms:
-2.333333334 + t = -1.452966316

Solving
-2.333333334 + t = -1.452966316

Solving for variable 't'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + t = -1.452966316 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + t = -1.452966316 + 2.333333334
t = -1.452966316 + 2.333333334

Combine like terms: -1.452966316 + 2.333333334 = 0.880367018
t = 0.880367018

Simplifying
t = 0.880367018


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.78629965, 0.880367018}

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