t^2-14t+4=0

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Solution for t^2-14t+4=0 equation: 


Simplifying
t2 + -14t + 4 = 0

Reorder the terms:
4 + -14t + t2 = 0

Solving
4 + -14t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -14t + -4 + t2 = 0 + -4

Reorder the terms:
4 + -4 + -14t + t2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -14t + t2 = 0 + -4
-14t + t2 = 0 + -4

Combine like terms: 0 + -4 = -4
-14t + t2 = -4

The t term is -14t.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14t + 49 + t2 = -4 + 49

Reorder the terms:
49 + -14t + t2 = -4 + 49

Combine like terms: -4 + 49 = 45
49 + -14t + t2 = 45

Factor a perfect square on the left side:
(t + -7)(t + -7) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(t + -7) equal to 6.708203933 and -6.708203933.


Subproblem 1
t + -7 = 6.708203933

Simplifying
t + -7 = 6.708203933

Reorder the terms:
-7 + t = 6.708203933

Solving
-7 + t = 6.708203933

Solving for variable 't'.

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

Add '7' to each side of the equation.
-7 + 7 + t = 6.708203933 + 7

Combine like terms: -7 + 7 = 0
0 + t = 6.708203933 + 7
t = 6.708203933 + 7

Combine like terms: 6.708203933 + 7 = 13.708203933
t = 13.708203933

Simplifying
t = 13.708203933


Subproblem 2
t + -7 = -6.708203933

Simplifying
t + -7 = -6.708203933

Reorder the terms:
-7 + t = -6.708203933

Solving
-7 + t = -6.708203933

Solving for variable 't'.

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

Add '7' to each side of the equation.
-7 + 7 + t = -6.708203933 + 7

Combine like terms: -7 + 7 = 0
0 + t = -6.708203933 + 7
t = -6.708203933 + 7

Combine like terms: -6.708203933 + 7 = 0.291796067
t = 0.291796067

Simplifying
t = 0.291796067


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {13.708203933, 0.291796067}

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