0=425-10t-t^2

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Solution for 0=425-10t-t^2 equation: 


Simplifying
0 = 425 + -10t + -1t2

Solving
0 = 425 + -10t + -1t2

Solving for variable 't'.

Combine like terms: 0 + -425 = -425
-425 + 10t + t2 = 425 + -10t + -1t2 + -425 + 10t + t2

Reorder the terms:
-425 + 10t + t2 = 425 + -425 + -10t + 10t + -1t2 + t2

Combine like terms: 425 + -425 = 0
-425 + 10t + t2 = 0 + -10t + 10t + -1t2 + t2
-425 + 10t + t2 = -10t + 10t + -1t2 + t2

Combine like terms: -10t + 10t = 0
-425 + 10t + t2 = 0 + -1t2 + t2
-425 + 10t + t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
-425 + 10t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '425' to each side of the equation.
-425 + 10t + 425 + t2 = 0 + 425

Reorder the terms:
-425 + 425 + 10t + t2 = 0 + 425

Combine like terms: -425 + 425 = 0
0 + 10t + t2 = 0 + 425
10t + t2 = 0 + 425

Combine like terms: 0 + 425 = 425
10t + t2 = 425

The t term is 10t.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10t + 25 + t2 = 425 + 25

Reorder the terms:
25 + 10t + t2 = 425 + 25

Combine like terms: 425 + 25 = 450
25 + 10t + t2 = 450

Factor a perfect square on the left side:
(t + 5)(t + 5) = 450

Calculate the square root of the right side: 21.213203436

Break this problem into two subproblems by setting 
(t + 5) equal to 21.213203436 and -21.213203436.


Subproblem 1
t + 5 = 21.213203436

Simplifying
t + 5 = 21.213203436

Reorder the terms:
5 + t = 21.213203436

Solving
5 + t = 21.213203436

Solving for variable 't'.

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

Add '-5' to each side of the equation.
5 + -5 + t = 21.213203436 + -5

Combine like terms: 5 + -5 = 0
0 + t = 21.213203436 + -5
t = 21.213203436 + -5

Combine like terms: 21.213203436 + -5 = 16.213203436
t = 16.213203436

Simplifying
t = 16.213203436


Subproblem 2
t + 5 = -21.213203436

Simplifying
t + 5 = -21.213203436

Reorder the terms:
5 + t = -21.213203436

Solving
5 + t = -21.213203436

Solving for variable 't'.

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

Add '-5' to each side of the equation.
5 + -5 + t = -21.213203436 + -5

Combine like terms: 5 + -5 = 0
0 + t = -21.213203436 + -5
t = -21.213203436 + -5

Combine like terms: -21.213203436 + -5 = -26.213203436
t = -26.213203436

Simplifying
t = -26.213203436


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {16.213203436, -26.213203436}

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