t^2+14t+15=0

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Solution for t^2+14t+15=0 equation: 


Simplifying
t2 + 14t + 15 = 0

Reorder the terms:
15 + 14t + t2 = 0

Solving
15 + 14t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 14t + -15 + t2 = 0 + -15

Reorder the terms:
15 + -15 + 14t + t2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 14t + t2 = 0 + -15
14t + t2 = 0 + -15

Combine like terms: 0 + -15 = -15
14t + t2 = -15

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 = -15 + 49

Reorder the terms:
49 + 14t + t2 = -15 + 49

Combine like terms: -15 + 49 = 34
49 + 14t + t2 = 34

Factor a perfect square on the left side:
(t + 7)(t + 7) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(t + 7) equal to 5.830951895 and -5.830951895.


Subproblem 1
t + 7 = 5.830951895

Simplifying
t + 7 = 5.830951895

Reorder the terms:
7 + t = 5.830951895

Solving
7 + t = 5.830951895

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 = 5.830951895 + -7

Combine like terms: 7 + -7 = 0
0 + t = 5.830951895 + -7
t = 5.830951895 + -7

Combine like terms: 5.830951895 + -7 = -1.169048105
t = -1.169048105

Simplifying
t = -1.169048105


Subproblem 2
t + 7 = -5.830951895

Simplifying
t + 7 = -5.830951895

Reorder the terms:
7 + t = -5.830951895

Solving
7 + t = -5.830951895

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 = -5.830951895 + -7

Combine like terms: 7 + -7 = 0
0 + t = -5.830951895 + -7
t = -5.830951895 + -7

Combine like terms: -5.830951895 + -7 = -12.830951895
t = -12.830951895

Simplifying
t = -12.830951895


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-1.169048105, -12.830951895}

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