2t^2+14t-3=3

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

Simplifying
2t2 + 14t + -3 = 3

Reorder the terms:
-3 + 14t + 2t2 = 3

Solving
-3 + 14t + 2t2 = 3

Solving for variable 't'.

Reorder the terms:
-3 + -3 + 14t + 2t2 = 3 + -3

Combine like terms: -3 + -3 = -6
-6 + 14t + 2t2 = 3 + -3

Combine like terms: 3 + -3 = 0
-6 + 14t + 2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 7t + t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 7t + t2)' equal to zero and attempt to solve:

Simplifying
-3 + 7t + t2 = 0

Solving
-3 + 7t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 7t + 3 + t2 = 0 + 3

Reorder the terms:
-3 + 3 + 7t + t2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 7t + t2 = 0 + 3
7t + t2 = 0 + 3

Combine like terms: 0 + 3 = 3
7t + t2 = 3

The t term is 7t.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7t + 12.25 + t2 = 3 + 12.25

Reorder the terms:
12.25 + 7t + t2 = 3 + 12.25

Combine like terms: 3 + 12.25 = 15.25
12.25 + 7t + t2 = 15.25

Factor a perfect square on the left side:
(t + 3.5)(t + 3.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(t + 3.5) equal to 3.905124838 and -3.905124838.

Subproblem 1
t + 3.5 = 3.905124838

Simplifying
t + 3.5 = 3.905124838

Reorder the terms:
3.5 + t = 3.905124838

Solving
3.5 + t = 3.905124838

Solving for variable 't'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + t = 3.905124838 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + t = 3.905124838 + -3.5
t = 3.905124838 + -3.5

Combine like terms: 3.905124838 + -3.5 = 0.405124838
t = 0.405124838

Simplifying
t = 0.405124838

Subproblem 2
t + 3.5 = -3.905124838

Simplifying
t + 3.5 = -3.905124838

Reorder the terms:
3.5 + t = -3.905124838

Solving
3.5 + t = -3.905124838

Solving for variable 't'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + t = -3.905124838 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + t = -3.905124838 + -3.5
t = -3.905124838 + -3.5

Combine like terms: -3.905124838 + -3.5 = -7.405124838
t = -7.405124838

Simplifying
t = -7.405124838

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.405124838, -7.405124838}
Solution
t = {0.405124838, -7.405124838}