45=15t+1.75t^2

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Solution for 45=15t+1.75t^2 equation: 


Simplifying
45 = 15t + 1.75t2

Solving
45 = 15t + 1.75t2

Solving for variable 't'.

Reorder the terms:
45 + -15t + -1.75t2 = 15t + -15t + 1.75t2 + -1.75t2

Combine like terms: 15t + -15t = 0
45 + -15t + -1.75t2 = 0 + 1.75t2 + -1.75t2
45 + -15t + -1.75t2 = 1.75t2 + -1.75t2

Combine like terms: 1.75t2 + -1.75t2 = 0.00
45 + -15t + -1.75t2 = 0.00

Begin completing the square.  Divide all terms by
-1.75 the coefficient of the squared term: 

Divide each side by '-1.75'.
-25.71428571 + 8.571428571t + t2 = 0

Move the constant term to the right:

Add '25.71428571' to each side of the equation.
-25.71428571 + 8.571428571t + 25.71428571 + t2 = 0 + 25.71428571

Reorder the terms:
-25.71428571 + 25.71428571 + 8.571428571t + t2 = 0 + 25.71428571

Combine like terms: -25.71428571 + 25.71428571 = 0.00000000
0.00000000 + 8.571428571t + t2 = 0 + 25.71428571
8.571428571t + t2 = 0 + 25.71428571

Combine like terms: 0 + 25.71428571 = 25.71428571
8.571428571t + t2 = 25.71428571

The t term is 8.571428571t.  Take half its coefficient (4.285714286).
Square it (18.36734694) and add it to both sides.

Add '18.36734694' to each side of the equation.
8.571428571t + 18.36734694 + t2 = 25.71428571 + 18.36734694

Reorder the terms:
18.36734694 + 8.571428571t + t2 = 25.71428571 + 18.36734694

Combine like terms: 25.71428571 + 18.36734694 = 44.08163265
18.36734694 + 8.571428571t + t2 = 44.08163265

Factor a perfect square on the left side:
(t + 4.285714286)(t + 4.285714286) = 44.08163265

Calculate the square root of the right side: 6.639400022

Break this problem into two subproblems by setting 
(t + 4.285714286) equal to 6.639400022 and -6.639400022.


Subproblem 1
t + 4.285714286 = 6.639400022

Simplifying
t + 4.285714286 = 6.639400022

Reorder the terms:
4.285714286 + t = 6.639400022

Solving
4.285714286 + t = 6.639400022

Solving for variable 't'.

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

Add '-4.285714286' to each side of the equation.
4.285714286 + -4.285714286 + t = 6.639400022 + -4.285714286

Combine like terms: 4.285714286 + -4.285714286 = 0.000000000
0.000000000 + t = 6.639400022 + -4.285714286
t = 6.639400022 + -4.285714286

Combine like terms: 6.639400022 + -4.285714286 = 2.353685736
t = 2.353685736

Simplifying
t = 2.353685736


Subproblem 2
t + 4.285714286 = -6.639400022

Simplifying
t + 4.285714286 = -6.639400022

Reorder the terms:
4.285714286 + t = -6.639400022

Solving
4.285714286 + t = -6.639400022

Solving for variable 't'.

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

Add '-4.285714286' to each side of the equation.
4.285714286 + -4.285714286 + t = -6.639400022 + -4.285714286

Combine like terms: 4.285714286 + -4.285714286 = 0.000000000
0.000000000 + t = -6.639400022 + -4.285714286
t = -6.639400022 + -4.285714286

Combine like terms: -6.639400022 + -4.285714286 = -10.925114308
t = -10.925114308

Simplifying
t = -10.925114308


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.353685736, -10.925114308}

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