34=-4.9t^2+64t

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Solution for 34=-4.9t^2+64t equation:


Simplifying
34 = -4.9t2 + 64t

Reorder the terms:
34 = 64t + -4.9t2

Solving
34 = 64t + -4.9t2

Solving for variable 't'.

Reorder the terms:
34 + -64t + 4.9t2 = 64t + -64t + -4.9t2 + 4.9t2

Combine like terms: 64t + -64t = 0
34 + -64t + 4.9t2 = 0 + -4.9t2 + 4.9t2
34 + -64t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
34 + -64t + 4.9t2 = 0.0

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

Divide each side by '4.9'.
6.93877551 + -13.06122449t + t2 = 0

Move the constant term to the right:

Add '-6.93877551' to each side of the equation.
6.93877551 + -13.06122449t + -6.93877551 + t2 = 0 + -6.93877551

Reorder the terms:
6.93877551 + -6.93877551 + -13.06122449t + t2 = 0 + -6.93877551

Combine like terms: 6.93877551 + -6.93877551 = 0.00000000
0.00000000 + -13.06122449t + t2 = 0 + -6.93877551
-13.06122449t + t2 = 0 + -6.93877551

Combine like terms: 0 + -6.93877551 = -6.93877551
-13.06122449t + t2 = -6.93877551

The t term is -13.06122449t.  Take half its coefficient (-6.530612245).
Square it (42.64889629) and add it to both sides.

Add '42.64889629' to each side of the equation.
-13.06122449t + 42.64889629 + t2 = -6.93877551 + 42.64889629

Reorder the terms:
42.64889629 + -13.06122449t + t2 = -6.93877551 + 42.64889629

Combine like terms: -6.93877551 + 42.64889629 = 35.71012078
42.64889629 + -13.06122449t + t2 = 35.71012078

Factor a perfect square on the left side:
(t + -6.530612245)(t + -6.530612245) = 35.71012078

Calculate the square root of the right side: 5.975794573

Break this problem into two subproblems by setting 
(t + -6.530612245) equal to 5.975794573 and -5.975794573.

Subproblem 1

t + -6.530612245 = 5.975794573 Simplifying t + -6.530612245 = 5.975794573 Reorder the terms: -6.530612245 + t = 5.975794573 Solving -6.530612245 + t = 5.975794573 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.530612245' to each side of the equation. -6.530612245 + 6.530612245 + t = 5.975794573 + 6.530612245 Combine like terms: -6.530612245 + 6.530612245 = 0.000000000 0.000000000 + t = 5.975794573 + 6.530612245 t = 5.975794573 + 6.530612245 Combine like terms: 5.975794573 + 6.530612245 = 12.506406818 t = 12.506406818 Simplifying t = 12.506406818

Subproblem 2

t + -6.530612245 = -5.975794573 Simplifying t + -6.530612245 = -5.975794573 Reorder the terms: -6.530612245 + t = -5.975794573 Solving -6.530612245 + t = -5.975794573 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.530612245' to each side of the equation. -6.530612245 + 6.530612245 + t = -5.975794573 + 6.530612245 Combine like terms: -6.530612245 + 6.530612245 = 0.000000000 0.000000000 + t = -5.975794573 + 6.530612245 t = -5.975794573 + 6.530612245 Combine like terms: -5.975794573 + 6.530612245 = 0.554817672 t = 0.554817672 Simplifying t = 0.554817672

Solution

The solution to the problem is based on the solutions from the subproblems. t = {12.506406818, 0.554817672}

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