7(t)=-10t^2+17t+1

Solution for 7(t)=-10t^2+17t+1 equation:

Simplifying
7(t) = -10t2 + 17t + 1

Reorder the terms:
7t = 1 + 17t + -10t2

Solving
7t = 1 + 17t + -10t2

Solving for variable 't'.

Reorder the terms:
-1 + 7t + -17t + 10t2 = 1 + 17t + -10t2 + -1 + -17t + 10t2

Combine like terms: 7t + -17t = -10t
-1 + -10t + 10t2 = 1 + 17t + -10t2 + -1 + -17t + 10t2

Reorder the terms:
-1 + -10t + 10t2 = 1 + -1 + 17t + -17t + -10t2 + 10t2

Combine like terms: 1 + -1 = 0
-1 + -10t + 10t2 = 0 + 17t + -17t + -10t2 + 10t2
-1 + -10t + 10t2 = 17t + -17t + -10t2 + 10t2

Combine like terms: 17t + -17t = 0
-1 + -10t + 10t2 = 0 + -10t2 + 10t2
-1 + -10t + 10t2 = -10t2 + 10t2

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

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

Divide each side by '10'.
-0.1 + -1t + t2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + -1t + 0.1 + t2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + -1t + t2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + -1t + t2 = 0 + 0.1
-1t + t2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
-1t + t2 = 0.1

The t term is -1t.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1t + 0.25 + t2 = 0.1 + 0.25

Reorder the terms:
0.25 + -1t + t2 = 0.1 + 0.25

Combine like terms: 0.1 + 0.25 = 0.35
0.25 + -1t + t2 = 0.35

Factor a perfect square on the left side:
(t + -0.5)(t + -0.5) = 0.35

Calculate the square root of the right side: 0.591607978

Break this problem into two subproblems by setting 
(t + -0.5) equal to 0.591607978 and -0.591607978.

Subproblem 1
t + -0.5 = 0.591607978

Simplifying
t + -0.5 = 0.591607978

Reorder the terms:
-0.5 + t = 0.591607978

Solving
-0.5 + t = 0.591607978

Solving for variable 't'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = 0.591607978 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = 0.591607978 + 0.5
t = 0.591607978 + 0.5

Combine like terms: 0.591607978 + 0.5 = 1.091607978
t = 1.091607978

Simplifying
t = 1.091607978

Subproblem 2
t + -0.5 = -0.591607978

Simplifying
t + -0.5 = -0.591607978

Reorder the terms:
-0.5 + t = -0.591607978

Solving
-0.5 + t = -0.591607978

Solving for variable 't'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + t = -0.591607978 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + t = -0.591607978 + 0.5
t = -0.591607978 + 0.5

Combine like terms: -0.591607978 + 0.5 = -0.091607978
t = -0.091607978

Simplifying
t = -0.091607978

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.091607978, -0.091607978}