t^2+17t-210=0

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Solution for t^2+17t-210=0 equation: 


Simplifying
t2 + 17t + -210 = 0

Reorder the terms:
-210 + 17t + t2 = 0

Solving
-210 + 17t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '210' to each side of the equation.
-210 + 17t + 210 + t2 = 0 + 210

Reorder the terms:
-210 + 210 + 17t + t2 = 0 + 210

Combine like terms: -210 + 210 = 0
0 + 17t + t2 = 0 + 210
17t + t2 = 0 + 210

Combine like terms: 0 + 210 = 210
17t + t2 = 210

The t term is 17t.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17t + 72.25 + t2 = 210 + 72.25

Reorder the terms:
72.25 + 17t + t2 = 210 + 72.25

Combine like terms: 210 + 72.25 = 282.25
72.25 + 17t + t2 = 282.25

Factor a perfect square on the left side:
(t + 8.5)(t + 8.5) = 282.25

Calculate the square root of the right side: 16.800297616

Break this problem into two subproblems by setting 
(t + 8.5) equal to 16.800297616 and -16.800297616.


Subproblem 1
t + 8.5 = 16.800297616

Simplifying
t + 8.5 = 16.800297616

Reorder the terms:
8.5 + t = 16.800297616

Solving
8.5 + t = 16.800297616

Solving for variable 't'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + t = 16.800297616 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + t = 16.800297616 + -8.5
t = 16.800297616 + -8.5

Combine like terms: 16.800297616 + -8.5 = 8.300297616
t = 8.300297616

Simplifying
t = 8.300297616


Subproblem 2
t + 8.5 = -16.800297616

Simplifying
t + 8.5 = -16.800297616

Reorder the terms:
8.5 + t = -16.800297616

Solving
8.5 + t = -16.800297616

Solving for variable 't'.

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

Add '-8.5' to each side of the equation.
8.5 + -8.5 + t = -16.800297616 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + t = -16.800297616 + -8.5
t = -16.800297616 + -8.5

Combine like terms: -16.800297616 + -8.5 = -25.300297616
t = -25.300297616

Simplifying
t = -25.300297616


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.300297616, -25.300297616}

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