t^2+90t+10=0

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Solution for t^2+90t+10=0 equation: 


Simplifying
t2 + 90t + 10 = 0

Reorder the terms:
10 + 90t + t2 = 0

Solving
10 + 90t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 90t + -10 + t2 = 0 + -10

Reorder the terms:
10 + -10 + 90t + t2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 90t + t2 = 0 + -10
90t + t2 = 0 + -10

Combine like terms: 0 + -10 = -10
90t + t2 = -10

The t term is 90t.  Take half its coefficient (45).
Square it (2025) and add it to both sides.

Add '2025' to each side of the equation.
90t + 2025 + t2 = -10 + 2025

Reorder the terms:
2025 + 90t + t2 = -10 + 2025

Combine like terms: -10 + 2025 = 2015
2025 + 90t + t2 = 2015

Factor a perfect square on the left side:
(t + 45)(t + 45) = 2015

Calculate the square root of the right side: 44.888751375

Break this problem into two subproblems by setting 
(t + 45) equal to 44.888751375 and -44.888751375.


Subproblem 1
t + 45 = 44.888751375

Simplifying
t + 45 = 44.888751375

Reorder the terms:
45 + t = 44.888751375

Solving
45 + t = 44.888751375

Solving for variable 't'.

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

Add '-45' to each side of the equation.
45 + -45 + t = 44.888751375 + -45

Combine like terms: 45 + -45 = 0
0 + t = 44.888751375 + -45
t = 44.888751375 + -45

Combine like terms: 44.888751375 + -45 = -0.111248625
t = -0.111248625

Simplifying
t = -0.111248625


Subproblem 2
t + 45 = -44.888751375

Simplifying
t + 45 = -44.888751375

Reorder the terms:
45 + t = -44.888751375

Solving
45 + t = -44.888751375

Solving for variable 't'.

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

Add '-45' to each side of the equation.
45 + -45 + t = -44.888751375 + -45

Combine like terms: 45 + -45 = 0
0 + t = -44.888751375 + -45
t = -44.888751375 + -45

Combine like terms: -44.888751375 + -45 = -89.888751375
t = -89.888751375

Simplifying
t = -89.888751375


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.111248625, -89.888751375}

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