t^2-14t+36=0

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Solution for t^2-14t+36=0 equation: 


Simplifying
t2 + -14t + 36 = 0

Reorder the terms:
36 + -14t + t2 = 0

Solving
36 + -14t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -14t + -36 + t2 = 0 + -36

Reorder the terms:
36 + -36 + -14t + t2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -14t + t2 = 0 + -36
-14t + t2 = 0 + -36

Combine like terms: 0 + -36 = -36
-14t + t2 = -36

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 = -36 + 49

Reorder the terms:
49 + -14t + t2 = -36 + 49

Combine like terms: -36 + 49 = 13
49 + -14t + t2 = 13

Factor a perfect square on the left side:
(t + -7)(t + -7) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(t + -7) equal to 3.605551275 and -3.605551275.


Subproblem 1
t + -7 = 3.605551275

Simplifying
t + -7 = 3.605551275

Reorder the terms:
-7 + t = 3.605551275

Solving
-7 + t = 3.605551275

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 = 3.605551275 + 7

Combine like terms: -7 + 7 = 0
0 + t = 3.605551275 + 7
t = 3.605551275 + 7

Combine like terms: 3.605551275 + 7 = 10.605551275
t = 10.605551275

Simplifying
t = 10.605551275


Subproblem 2
t + -7 = -3.605551275

Simplifying
t + -7 = -3.605551275

Reorder the terms:
-7 + t = -3.605551275

Solving
-7 + t = -3.605551275

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 = -3.605551275 + 7

Combine like terms: -7 + 7 = 0
0 + t = -3.605551275 + 7
t = -3.605551275 + 7

Combine like terms: -3.605551275 + 7 = 3.394448725
t = 3.394448725

Simplifying
t = 3.394448725


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {10.605551275, 3.394448725}

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