-73.3=-4.905t^2+2.45t

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Solution for -73.3=-4.905t^2+2.45t equation:


Simplifying
-73.3 = -4.905t2 + 2.45t

Reorder the terms:
-73.3 = 2.45t + -4.905t2

Solving
-73.3 = 2.45t + -4.905t2

Solving for variable 't'.

Reorder the terms:
-73.3 + -2.45t + 4.905t2 = 2.45t + -2.45t + -4.905t2 + 4.905t2

Combine like terms: 2.45t + -2.45t = 0.00
-73.3 + -2.45t + 4.905t2 = 0.00 + -4.905t2 + 4.905t2
-73.3 + -2.45t + 4.905t2 = -4.905t2 + 4.905t2

Combine like terms: -4.905t2 + 4.905t2 = 0.000
-73.3 + -2.45t + 4.905t2 = 0.000

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

Divide each side by '4.905'.
-14.94393476 + -0.499490316t + t2 = 0

Move the constant term to the right:

Add '14.94393476' to each side of the equation.
-14.94393476 + -0.499490316t + 14.94393476 + t2 = 0 + 14.94393476

Reorder the terms:
-14.94393476 + 14.94393476 + -0.499490316t + t2 = 0 + 14.94393476

Combine like terms: -14.94393476 + 14.94393476 = 0.00000000
0.00000000 + -0.499490316t + t2 = 0 + 14.94393476
-0.499490316t + t2 = 0 + 14.94393476

Combine like terms: 0 + 14.94393476 = 14.94393476
-0.499490316t + t2 = 14.94393476

The t term is -0.499490316t.  Take half its coefficient (-0.249745158).
Square it (0.06237264394) and add it to both sides.

Add '0.06237264394' to each side of the equation.
-0.499490316t + 0.06237264394 + t2 = 14.94393476 + 0.06237264394

Reorder the terms:
0.06237264394 + -0.499490316t + t2 = 14.94393476 + 0.06237264394

Combine like terms: 14.94393476 + 0.06237264394 = 15.00630740394
0.06237264394 + -0.499490316t + t2 = 15.00630740394

Factor a perfect square on the left side:
(t + -0.249745158)(t + -0.249745158) = 15.00630740394

Calculate the square root of the right side: 3.873797543

Break this problem into two subproblems by setting 
(t + -0.249745158) equal to 3.873797543 and -3.873797543.

Subproblem 1

t + -0.249745158 = 3.873797543 Simplifying t + -0.249745158 = 3.873797543 Reorder the terms: -0.249745158 + t = 3.873797543 Solving -0.249745158 + t = 3.873797543 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.249745158' to each side of the equation. -0.249745158 + 0.249745158 + t = 3.873797543 + 0.249745158 Combine like terms: -0.249745158 + 0.249745158 = 0.000000000 0.000000000 + t = 3.873797543 + 0.249745158 t = 3.873797543 + 0.249745158 Combine like terms: 3.873797543 + 0.249745158 = 4.123542701 t = 4.123542701 Simplifying t = 4.123542701

Subproblem 2

t + -0.249745158 = -3.873797543 Simplifying t + -0.249745158 = -3.873797543 Reorder the terms: -0.249745158 + t = -3.873797543 Solving -0.249745158 + t = -3.873797543 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.249745158' to each side of the equation. -0.249745158 + 0.249745158 + t = -3.873797543 + 0.249745158 Combine like terms: -0.249745158 + 0.249745158 = 0.000000000 0.000000000 + t = -3.873797543 + 0.249745158 t = -3.873797543 + 0.249745158 Combine like terms: -3.873797543 + 0.249745158 = -3.624052385 t = -3.624052385 Simplifying t = -3.624052385

Solution

The solution to the problem is based on the solutions from the subproblems. t = {4.123542701, -3.624052385}

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