t^2-14t-45=0

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Solution for t^2-14t-45=0 equation: 


Simplifying
t2 + -14t + -45 = 0

Reorder the terms:
-45 + -14t + t2 = 0

Solving
-45 + -14t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + -14t + 45 + t2 = 0 + 45

Reorder the terms:
-45 + 45 + -14t + t2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -14t + t2 = 0 + 45
-14t + t2 = 0 + 45

Combine like terms: 0 + 45 = 45
-14t + t2 = 45

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 = 45 + 49

Reorder the terms:
49 + -14t + t2 = 45 + 49

Combine like terms: 45 + 49 = 94
49 + -14t + t2 = 94

Factor a perfect square on the left side:
(t + -7)(t + -7) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(t + -7) equal to 9.695359715 and -9.695359715.


Subproblem 1
t + -7 = 9.695359715

Simplifying
t + -7 = 9.695359715

Reorder the terms:
-7 + t = 9.695359715

Solving
-7 + t = 9.695359715

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 = 9.695359715 + 7

Combine like terms: -7 + 7 = 0
0 + t = 9.695359715 + 7
t = 9.695359715 + 7

Combine like terms: 9.695359715 + 7 = 16.695359715
t = 16.695359715

Simplifying
t = 16.695359715


Subproblem 2
t + -7 = -9.695359715

Simplifying
t + -7 = -9.695359715

Reorder the terms:
-7 + t = -9.695359715

Solving
-7 + t = -9.695359715

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 = -9.695359715 + 7

Combine like terms: -7 + 7 = 0
0 + t = -9.695359715 + 7
t = -9.695359715 + 7

Combine like terms: -9.695359715 + 7 = -2.695359715
t = -2.695359715

Simplifying
t = -2.695359715


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {16.695359715, -2.695359715}

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