3t^2-14t+3=0

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


Simplifying
3t2 + -14t + 3 = 0

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

Solving
3 + -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'.
1 + -4.666666667t + t2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -4.666666667t + -1 + t2 = 0 + -1

Reorder the terms:
1 + -1 + -4.666666667t + t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4.666666667t + t2 = 0 + -1
-4.666666667t + t2 = 0 + -1

Combine like terms: 0 + -1 = -1
-4.666666667t + t2 = -1

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 = -1 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667t + t2 = -1 + 5.444444448

Combine like terms: -1 + 5.444444448 = 4.444444448
5.444444448 + -4.666666667t + t2 = 4.444444448

Factor a perfect square on the left side:
(t + -2.333333334)(t + -2.333333334) = 4.444444448

Calculate the square root of the right side: 2.108185108

Break this problem into two subproblems by setting 
(t + -2.333333334) equal to 2.108185108 and -2.108185108.

Subproblem 1

t + -2.333333334 = 2.108185108 Simplifying t + -2.333333334 = 2.108185108 Reorder the terms: -2.333333334 + t = 2.108185108 Solving -2.333333334 + t = 2.108185108 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 = 2.108185108 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + t = 2.108185108 + 2.333333334 t = 2.108185108 + 2.333333334 Combine like terms: 2.108185108 + 2.333333334 = 4.441518442 t = 4.441518442 Simplifying t = 4.441518442

Subproblem 2

t + -2.333333334 = -2.108185108 Simplifying t + -2.333333334 = -2.108185108 Reorder the terms: -2.333333334 + t = -2.108185108 Solving -2.333333334 + t = -2.108185108 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 = -2.108185108 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + t = -2.108185108 + 2.333333334 t = -2.108185108 + 2.333333334 Combine like terms: -2.108185108 + 2.333333334 = 0.225148226 t = 0.225148226 Simplifying t = 0.225148226

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.441518442, 0.225148226}

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