300=0.0089t^2+1.1149t+78.4491

Solution for 300=0.0089t^2+1.1149t+78.4491 equation:

Simplifying
300 = 0.0089t2 + 1.1149t + 78.4491

Reorder the terms:
300 = 78.4491 + 1.1149t + 0.0089t2

Solving
300 = 78.4491 + 1.1149t + 0.0089t2

Solving for variable 't'.

Combine like terms: 300 + -78.4491 = 221.5509
221.5509 + -1.1149t + -0.0089t2 = 78.4491 + 1.1149t + 0.0089t2 + -78.4491 + -1.1149t + -0.0089t2

Reorder the terms:
221.5509 + -1.1149t + -0.0089t2 = 78.4491 + -78.4491 + 1.1149t + -1.1149t + 0.0089t2 + -0.0089t2

Combine like terms: 78.4491 + -78.4491 = 0.0000
221.5509 + -1.1149t + -0.0089t2 = 0.0000 + 1.1149t + -1.1149t + 0.0089t2 + -0.0089t2
221.5509 + -1.1149t + -0.0089t2 = 1.1149t + -1.1149t + 0.0089t2 + -0.0089t2

Combine like terms: 1.1149t + -1.1149t = 0.0000
221.5509 + -1.1149t + -0.0089t2 = 0.0000 + 0.0089t2 + -0.0089t2
221.5509 + -1.1149t + -0.0089t2 = 0.0089t2 + -0.0089t2

Combine like terms: 0.0089t2 + -0.0089t2 = 0.0000
221.5509 + -1.1149t + -0.0089t2 = 0.0000

Begin completing the square.  Divide all terms by
-0.0089 the coefficient of the squared term: 

Divide each side by '-0.0089'.
-24893.35955 + 125.2696629t + t2 = 0

Move the constant term to the right:

Add '24893.35955' to each side of the equation.
-24893.35955 + 125.2696629t + 24893.35955 + t2 = 0 + 24893.35955

Reorder the terms:
-24893.35955 + 24893.35955 + 125.2696629t + t2 = 0 + 24893.35955

Combine like terms: -24893.35955 + 24893.35955 = 0.00000
0.00000 + 125.2696629t + t2 = 0 + 24893.35955
125.2696629t + t2 = 0 + 24893.35955

Combine like terms: 0 + 24893.35955 = 24893.35955
125.2696629t + t2 = 24893.35955

The t term is 125.2696629t.  Take half its coefficient (62.63483145).
Square it (3923.122111) and add it to both sides.

Add '3923.122111' to each side of the equation.
125.2696629t + 3923.122111 + t2 = 24893.35955 + 3923.122111

Reorder the terms:
3923.122111 + 125.2696629t + t2 = 24893.35955 + 3923.122111

Combine like terms: 24893.35955 + 3923.122111 = 28816.481661
3923.122111 + 125.2696629t + t2 = 28816.481661

Factor a perfect square on the left side:
(t + 62.63483145)(t + 62.63483145) = 28816.481661

Calculate the square root of the right side: 169.754180099

Break this problem into two subproblems by setting 
(t + 62.63483145) equal to 169.754180099 and -169.754180099.

Subproblem 1
t + 62.63483145 = 169.754180099

Simplifying
t + 62.63483145 = 169.754180099

Reorder the terms:
62.63483145 + t = 169.754180099

Solving
62.63483145 + t = 169.754180099

Solving for variable 't'.

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

Add '-62.63483145' to each side of the equation.
62.63483145 + -62.63483145 + t = 169.754180099 + -62.63483145

Combine like terms: 62.63483145 + -62.63483145 = 0.00000000
0.00000000 + t = 169.754180099 + -62.63483145
t = 169.754180099 + -62.63483145

Combine like terms: 169.754180099 + -62.63483145 = 107.119348649
t = 107.119348649

Simplifying
t = 107.119348649

Subproblem 2
t + 62.63483145 = -169.754180099

Simplifying
t + 62.63483145 = -169.754180099

Reorder the terms:
62.63483145 + t = -169.754180099

Solving
62.63483145 + t = -169.754180099

Solving for variable 't'.

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

Add '-62.63483145' to each side of the equation.
62.63483145 + -62.63483145 + t = -169.754180099 + -62.63483145

Combine like terms: 62.63483145 + -62.63483145 = 0.00000000
0.00000000 + t = -169.754180099 + -62.63483145
t = -169.754180099 + -62.63483145

Combine like terms: -169.754180099 + -62.63483145 = -232.389011549
t = -232.389011549

Simplifying
t = -232.389011549

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {107.119348649, -232.389011549}